6.11: Buying or Leasing a Car
- Evaluate basics of car purchasing.
- Compute purchase payments and identify the related interest cost.
- Evaluate the basics of leasing a car.
- Identify and contrast the pros and cons of purchasing versus leasing a car.
- Investigate the types of car insurance.
- Solve application problems involving owning and maintaining a car.
There are people who don’t need a car and won’t purchase one. But for many people, whether or not to have a car is not a question. Having a car is a basic necessity for these people.
Obtaining a car can be daunting. The models, the features, the additional costs, and finding funding are all steps that need to be taken. One of the big decisions is whether to buy the car or to lease the car. This section will address some of the issues associated with each option.
The Basics of Car Purchasing
The biggest questions you will answer before purchasing a car are, what do you want and what do you need?
Does it have to be new? Does it have to be a make and model you are familiar with? Does it have to have assisted driving? What other details are important to you? For a new vehicle, every feature beyond standard features comes with additional cost, which leads to the question that constrains all of your decisions about a car. How much can you afford to spend on a car?
What you can afford must include insurance costs (discussed later in this section) and maintenance and upkeep. Once you have this in mind, you can search for a car that matches, as closely as possible, what you want and can afford. Most, if not all, dealers have websites that you can search through to identify the car you want. If new cars are not affordable, used cars cost less but come with the wear and tear of use.
The sticker price of the car, called the manufacturer’s suggested retail price (MSRP), or the negotiated price you arrive at, isn’t the end of the cost to buying a car. There are many fees that accompany the purchase of the car, and perhaps even sales tax. These include but aren’t necessarily limited to the following:
- the title and registration fee , which includes registering your car with the state, getting the license plate, and assigning the title of the car to the lender. This cannot be avoided.
- a destination fee , which covers the cost of delivering the vehicle to the dealer
- a documentation fee , sometimes referred to a processing fee of handling fee, is the cost of all the paperwork the dealer did to get you the car
- a dealer preparation fee , which is for washing the car and other preparation of that sort. You should try to negotiate that out of the cost of the dealer tries to charge for that
- extended warranties and maintenance plans, which help cover some of the costs of caring for the car.
- Sales tax.
You could pay for these immediately, but they are often added to the financing of the car, meaning they become part of the principal of your loan.
Nichole negotiates with her car dealership so that the price is $21,800. She needs to pay the 6.75% sales tax on the car. Other fees are $31.00 for title and registration, $1,000 in destination fees, and a documentation fee of $175. What is the total cost of Nichole’s car?
- Answer
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We add the car’s sales cost, sales tax and all other fees to arrive at this value. The sales tax is 6.75% on the price she negotiated, so is . Adding these up, we have a total cost of .
Luther negotiates for the price of his car, reaching agreement at $28,975. He needs to pay 8% in sales tax, 2.1% in ownership tax, a $950 destination fee, processing fees totaling $370, and registration fee of $617. What is the total cost for Luther’s purchase?
One way to bring down payments on a car is to provide a down payment or a trade in. This is money applied to the purchase price before financing happens. Be warned, the sales tax applies to the full purchase price! If you reduce the amount financed, the payments respond by going down. This often becomes part of the negotiating process.
Sophia negotiates a $19,800 price for her new car. The sales tax is 9.5% in her area, and the dealership charges her $300 in documentation fees. Her title, plates, and registration come to $321.50. The dealership adds to this a destination fee of $1,100. If she places a down payment of $5,000 on the car, what is the total she will finance for the car?
- Answer
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The price was $19,800. The sales tax of 9.5% is based on this number. The sales tax comes to . Adding all the fees to the price and the sales tax brings the total cost of the car to . Her down payment is applied to this number, so the $5,000 is subtracted from $23,402.50. The subtraction yields the amount to be financed, which is $18,402.50.
Carlos buys a car with a negotiated price of $36,250. The sales tax in his region is 6.5%. The dealer charges a $1,200 destination fee and a $450 documentation fee. He must pay for title, registration, and license plates, which come to $21.50. If he has a $7,500 down payment, how much will he have to finance?
When purchasing a car, the total cost to obtain the car is not the only factor in your monthly price. You will also pay an interest rate for the loan you obtain. The interest rate you will get is dependent on your credit score (see The Basics of Loans). But you can choose from different lenders. The dealership will likely offer to finance your car loan. Frequently, dealerships offer special financing with very low rates. This is to help move inventory, and may indicate their desire to make sales. This might make negotiating easier. Even if the dealership offers financing, check with your bank or credit union to determine the interest rates they are offering. To reduce your payments, choose the lowest rate you can find.
Purchase Payments and Interest
Whether or not you buy a new car or a used car, if you finance the purchase, you are taking out a loan. The interest rates available for used cards are frequently higher than those for new cars. These loan payments work exactly the same way as other loans do as far as payments are concerned. The payment function comes from The Basics of Loans. The difference between financing a new car or a used car is that financing a new car typically comes with a lower interest rate and a longer term that financing a used car.
The payment, , per period to pay off a loan with beginning principal is , where is the annual interest rate in decimal form, is the term in years, and is the number of payments per year (typically, loans are paid monthly making = 12).
Note, payment to lenders is always rounded up to the next penny.
Often, the formula takes the form , where is the interest rate per period (annual rate divided by the number of periods per year), and is the total number of payments to be made.
In the following, calculate the monthly payment using the given total to be financed, the interest rate, and the term of the car loan.
- Total to be financed is $31,885, interest rate is 2.9%, for 5 years.
- Total to be financed is $22,778, interest rate is 4.5%, for 6 years.
- Answer
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The amount to be financed is the principal,
, which is $31,885. The rate
is 0.029, and the term is
= 5 years. These are monthly payments, so
= 12. Substituting and calculating, we find the monthly payment to be
-
The amount to be financed is the principal,
, which is $22,778. The rate
is 0.045, and the term is
= 6 years. These are monthly payments, so
= 12. Substituting and calculating, we find the monthly payment to be
-
The amount to be financed is the principal,
, which is $31,885. The rate
is 0.029, and the term is
= 5 years. These are monthly payments, so
= 12. Substituting and calculating, we find the monthly payment to be
In the following, calculate the monthly payment using the given total to be financed, the interest rate, and the term of the car loan.
Total to be financed is $18,325, interest rate is 6.75%, for 4 years.
Total to be financed is $41,633, interest rate is 3.9%, for 6 years.
Calculate the monthly payment for the used car if the total to be financed is $16,990, the interest rate is 7.5%, and the loan term is 3 years.
- Answer
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The amount to be financed is the principal, , which is $16,990. The rate is 0.075, and the term is = 3 years. These are monthly payments, so = 12. Substituting and calculating, we find the monthly payment to be
Calculate the monthly payment for a car loan that has $21,845 being financed at an interest rate of 6.3% for 4 years.
The Basics of Leasing a Car
Leasing a car is an alternative to purchasing a car. It is still a loan, and acts like one in many respects. They typically last either 24 months or 36 months, though other terms are available. Leases also come with mileage limits, frequently 10,000, 12,000, or 15,000 miles per year. When the lease is over, the car is returned to the dealer. At that time there may be fees that have to be paid, such as for damage to the car or for extra miles driven over the limit.
There are two components to lease costs. One is the monthly payment for the lease. The other is the fees for leasing, These often are paid before the lease is complete. These include:
- a down payment, which is your initial payment that is applied to the price of the car. It reduces the amount you finance, much the same as when you purchase a car. It is recommended that this be negotiated away.
- the acquisition fee , sometimes called the bank fee. This is the money charge for the company to set up the lease. It is essentially a paperwork fee. It is not likely that this can be negotiated.
- a security deposit , which might be required. It is about the same as 1 month’s payment for the lease. The deposit is returned to you if the car is in good shape at the end. This can be negotiated away.
- disposition fees , which cover the cost the company will incur when they take your car back and are typically between $200 and $450.
- the title, registration, and license fees, just as with the purchase of a car.
- sales tax, which will likely be applied. The sales tax only covers the depreciated portion of the car (more on depreciation later) in many states. Since this depends on the state in which the car is leased, you should determine the sales tax rules for where you lease the car.
As you can imagine, this can come to a fairly high dollar amount.
Donna wants to lease a Subaru Outback in Eden, New York. Find the total cost of obtaining her lease if there is no down payment, $175.00 in acquisition fees, a security deposit of $300.00, $350.00 in disposition fees, $102.50 in title and registration fees, and sales tax of $3,536.05.
- Answer
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Adding these values together we find the total cost is $4,463.55.
RJ wants to lease a Tahoe in Salt Lake City, Utah. Find the total cost of obtaining his lease if he has a $5,000.00 down payment, $225 in acquisition fees, a security deposit of $750.00, $500.00 in disposition fees, and sales tax of $4,092.
Zollie Frank and Armund Shoen founded one of the original leasing companies, Four Wheels, in 1939. Their company leased automobiles to corporations. They began by leasing 5 cars to the Petrolager pharmaceutical company in year one. This saved Petrolager money and provided a steady cash flow to the Four Wheels business. In year two, the number of cars leased to Petrolager was 75. Their new idea was to lease cars directly to companies for one year. Previously, such companies might pay for mileage, gas, and a partial down payment. Sadly, the salesmen who were being so helped often left the company before the car was paid for, and so the company lost the down payment money.
The lease was for $45 per month per car for one year.
You have some obligations when you lease a car. You must keep the car in good condition, cleaned, maintained, and free of anything more than minor damage. If the car is in poor condition when the car is returned, you will be responsible for the cost to bring the car to an acceptable condition. You are also expected to keep the mileage under its limit. If you go over, you will pay 10 to 25 cents per mile over.
Lease Payments
Lease payments are similar to regular loan payments, but have some other details. Calculating a lease payment involves knowing the following values:
- The price of the car. This is the cost you would pay for the car after applying all discounts, incentives, and negotiations.
- Residual Value. This is the manufacturer's estimate of the car's value after a set period of time. The residual value is expressed as a percentage of the manufacturer’s suggested retail price (MSRP).
- Months. This is the length of the lease. Most leases are either 24- or 36-month leases, but other terms are available.
- Monthly Depreciation . The monthly depreciation is the difference between the price of the car and the residual value, divided by the number of months of the lease, and represents the monthly loss of value of the car while it’s being used.
- Money Factor (MF). This is the interest rate, but expressed in a different way for a lease. Converting from the money factor to the annual percentage rate (APR) is done by multiplying the MF by 2400. Naturally, converting an APR to a MF is done by dividing the APR by 2400.
The monthly depreciation for a car, MD, is , is the price paid for the car, is the residual value of the car, and is the number of months of the lease.
The annual percentage rate for a lease is , where MF is the money factor of the lease. The MF for a lease is .
- The purchase price of a car is $25,000. Its residual price is $14,500. What is its monthly depreciation for a 36-month lease?
- The purchase price of a car is $30,000. Its residual price is $18,600. What is its monthly depreciation for a 24-month lease?
- Answer
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- The monthly depreciation formula is , Substituting $25,000 for , $14,500 for , and 36 for , we find MD to be .
- The monthly depreciation formula is , Substituting $30,000 for , $18,600 for , and 24 for , we find MD to be .
The purchase price of a car is $27,500. Its residual price is $17,875.00. What is its monthly depreciation for a 24-month lease?
- Find the annual percentage rate if the money factor is 0.00001875.
- Find the money factor if the APR is 6.25%.
- Answer
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- The APR is the money factor times 2400, so . Expressed as a percentage, the APR is 4.5%.
- The MF is the APR divided by 2400, so .
Find the annual percentage rate if the money factor is \(0.00001208\overline 3 \).
Find the money factor if the APR is 7.9%.
Once the values above are found, the payment for the lease can be calculated.
The payment, , for a lease is , where is the price paid for the car, is the residual value of the car, is the number of months of the lease, and MF is the money factor for the lease.
Calculate the lease payments for car with the following price, residual price, length of lease, and money factor or APR.
- Price is $28,344, residual price is $18,140.16, 24-month lease, money factor is 0.000025.
- Price is $22,500, residual price is $13,050, 36-month lease, APR is 7.5%.
- Answer
-
-
Substituting the values
= $28,344,
= $18,140.16,
= 24 and MF = 0.000025 into the formula and calculating, the monthly lease payment is
-
Given the APR, we find the MF which is
. Substituting the values
= $28,344,
= $18,140.16,
= 24 and the MF into the formula and calculating, the monthly lease payment is
-
Substituting the values
= $28,344,
= $18,140.16,
= 24 and MF = 0.000025 into the formula and calculating, the monthly lease payment is
Calculate the lease payments for car with the following price, residual price, length of lease, and money factor or APR.
Price is $38,750, residual price is $18,140.16, 36-month lease, money factor is 0.000035.
Price is $45,600, residual price is $21,312.50, 24-month lease, APR is 11.7%.
Comparing Purchasing and Leasing
When deciding to buy or lease a car, the differences between the two options should be carefully evaluated. The following is a list of points of comparison between the two.
- The payments for a lease are likely less than the payment for purchasing.
- When leasing, you get a new car after the lease term is over, typically 24 or 36 months. Buying the car means the same car is driven until it is re-sold and a new one bought. Essentially, leasing a car is equivalent to renting a car.
- The leased car is new, so all warrantees are in force and you drive the car during its best years. When the car is purchased, it may be kept past its warrantees and may be driven until it is quite old.
- Each time you lease a new car, all the fees and taxes must be paid again. When buying a car, these fees are only paid once.
- Leasing contracts carry restrictions on the mileage you can drive per year, and going over incurs more cost at the end of the lease. Buying the car means no such mileage limits.
- When leasing, you are obligated to keep the vehicle in good condition and maintained according to the dealer’s schedule. Some dealerships will even pay for oil changes over the life of the lease. When the car is purchased, the upkeep schedule is the choice of the owner.
- When a car is purchased and kept for long enough, the warranty expires and the owner is responsible for all maintenance items and repairs. The warrantee for a car won’t expire during the lease term.
- When a new car is purchased and the loan is paid off the car is still owned by the buyer and may be traded in when a new car is to be purchased. When leasing, the car is returned to the dealer when the lease term is over.
When deciding between the two, you are choosing between these features. If you aren’t willing to drive an older car or deal with the upkeep that accompanies an older car, you may want to lease. This means you will need to pay those beginning costs each time the lease is up. If you want to own the car after the payments are over, then you may want to buy a car. This means you are paying for all the upkeep after the warrantees expire, but you have no limits on mileage and own the car at the end. It really depends on your preferences.
In the following, determine if a lease or purchase of a car is better.
- Joyce is concerned with large repairs and does not want to deal with them.
- Maurice prefers to drive newer cars.
- Answer
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- Since Joyce does not want to deal with repairs, so leasing would be a better choice. This way, the warranty covers most of the big repairs that could need to be done.
- Since Maurice likes to drive new cars, leasing is a better option, since he will lease a new car every 2 to 3 years.
Christopher does a lot of driving, averaging over 20,000 miles per year.
John eventually wants to not make car payments.
Car Insurance
Car insurance is meant to cover costs associated with accidents involving cars. Most states (all except New Hampshire and Virginia) require some insurance. Without insurance, the state may not let you get a license for your car or register your car. Your state’s requirements can be hard to follow. Fortunately, insurance companies and brokers will make sure your insurance is sufficient for your state and will warn you if you try to not meet the requirements. Of course, they may offer more than what is sufficient, so it is your responsibility to determine how much coverage you want, as long as the minimum insurance requirements are met. The cost of insurance should be accounted for when evaluating the affordability of buying or leasing a car.
Whether your car is leased or owned, you do need insurance. This contributes to the cost of having the vehicle. Leasing or owning makes no difference to the insurance company you choose, because they are insuring you based on what you are driving, your driving record, and other information about you including where you live and your age. These insurance policies have many components that address different costs that can come from auto accidents. This may make details confusing, and you may not realize what you are paying for until you must use it. Here is a brief outline of the different components of auto insurance, many of which are required by the state that issues your driver’s license.
- Liability insurance is mandatory coverage in most states. Liability insurance covers property damage and injuries to others should you be found legally responsible for an accident. You are required to have the minimum amount of coverage, as determined by your state, in both areas.
- Collision insurance is insurance covering the damage caused to your car if involved in an accident with another vehicle.
- Comprehensive insurance is an extra level of coverage if involved in an accident with another vehicle and covers other things like theft, vandalism, fire, or weather events as outlined in your policy. There is a deductible assigned to each type of insurance, an amount that you pay out of pocket before your comprehensive coverage takes effect. Comprehensive insurance is often required if you lease or finance the purchase of a vehicle.
- Uninsured or underinsured motorist insurance: If you are hit by an uninsured or underinsured motorist, this insurance will help pay medical bills and damage to your car.
- Medical payments insurance is mandatory in some states and helps pay for medical costs associated with an accident, regardless of who is at fault.
- Personal injury protection insurance is coverage for certain medical bills and other expenses due to a car accident. Other covered expenses may include loss of income or childcare, depending on your policy.
- Gap insurance is designed to cover the gap between what is owed on the car and what the car is worth in the event your car is a total loss.
- Rental reimbursement insurance is coverage for a rental car while your car is under repair resulting from an accident.
You can also purchase other special insurance policies, such as classic car insurance, new car replacement insurance, and sound system replacement insurance, to name a few. It is important that you determine exactly what you need, as insurance policies can be expensive and vary according to your age, driving history, and where you live.
- Which component of insurance pays if you are in an accident with a motorist without insurance?
- Which component of insurance pays for the remaining principal owed on your car in the case of a total loss?
- Answer
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- Uninsured motorist insurance covers accidents with those who have no insurance.
- Gap insurance will cover the gap between what is owed on the car and what it is worth if an accident results in a total loss.
Which component of insurance covers medical bills in the event of an accident?
Which component of insurance pays for costs to others if you have an accident and are found legally responsible for those damages?
If your car payment is $287.50 per month and your car insurance is $930 every 6 months, what is the cost of the car per month when accounting for the insurance?
- Answer
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The cost of the car including insurance is the monthly payment, $287.50, plus the monthly cost of the insurance. The insurance cost per month is since the insurance cost is for every 6 months. Adding those the cost with insurance is $442.50.
If your car payment is $410.86 per month and your car insurance is $2,190 per year, what is the cost of the car per month when accounting for the insurance?
Maintaining a Car
Cars are not a buy it and forget it item. They require upkeep, which adds to the cost of owning the car. Tires, brakes, and wipers need replacing. Oli changes, inspections, so many things other than gasoline. Below is a list of some maintenance requirements for cars, along with cost and roughly how often they should happen.
| Maintenance | Frequency | Cost Range |
|---|---|---|
| New Tires | Every 5 years | $25–$300 per tire |
| Oil Change | Every 3,000–6,000 miles | $35–$75 |
| Wipers | Every 6–12 months | $20–$40 |
| Inspection | Annual | $10–$50 |
| Brake pads | 10,000–20,000 miles | $200–$300 |
| Air Filter | 15,000–30,000 miles | $35–$80 |
When designing a budget, these expected costs should be accounted for. Extra money per month should be saved in addition to this budget category, to handle unanticipated, and perhaps very costly, repairs.
Estella needs to budget for her car maintenance. She expects to buy new tires each 4 years, which will cost her $480 to replace them all. Oil changes near her cost $49.99, and she believes she will get one every 4 months. Her inspection costs $15 per year. Wipers for her car cost $95 for all three and she anticipates changing them every year. She drives less than 30,000 miles per year, so she plans to replace the air filter once per year. The air filter for her car costs $57.50. How much should she budget per month to cover these costs?
- Answer
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Her yearly costs are the wipers, inspection, and tires, which total $167.50. Tires will be bought every 5 years, so per year she should budget $96. Her oil changes, which will happen three times per year, cost $49.99 each, so she’ll spend $149.97 for the year on oil changes. Adding these up, her yearly budget should include $413.47 for maintenance. Dividing by 12 gives the monthly budget for maintenance, which is $34.46 (rounded up to the next penny).
Natalie needs to budget for her car maintenance. She expects to buy new tires each 5 years, which will cost her $390 to replace them all. Oil changes near her cost $59.99, and she believes she will get one every 3 months. Her inspection costs $25 per year. Wipers for her car cost $115 for all three and she anticipates changing them every year. She drives less than 30,000 miles per year, so she plans to replace the air filter once per year. The air filter for her car costs $46.25. How much should she budget per month to cover these costs?
Check Your Understanding
- What is destination fee?
- What is a title and registration fee?
- Calculate the monthly payment if the total to be financed is $34,570, the interest rate is 3.5%, for 5 years.
- What might be different for a used car loan and a new car loan?
- What fees are similar between leasing a car and buying a car?
- If the cost of a car is $30,000, and the residual value of the car after 3 years is $18,000, what is the monthly depreciation for the car?
- If the money factor for a lease is 0.000015625, what is the annual interest rate?
- For people who do not mind driving an older car or maintaining a car, which is preferable, a lease or purchasing?
- What does collision insurance cover?


11.5: Physiology of the Lymphatic and Immune Systems
Immune Response
There are two basic processes in which the human body defends against microorganisms that cause infection, referred to as a nonspecific, innate immune response and a specific, adaptive immune response.
Innate Immune Response
The nonspecific, innate immune response (ĭn-NĀT i-MŪN ri-SPONS) refers to defenses that target invading pathogens in a nonspecific manner. It is called “innate” because it is present from the moment we are born. Pathogens (PĂTH-ō-jĕnz) refer to bacteria, viruses, or other microorganisms that can cause infection and disease. The innate immune response includes physical barriers, inflammation, and fever. [1]
Physical Barriers
Physical barriers are the body’s basic defenses against infection. These physical barriers are also referred to as the body’s first line of defense. They include intact skin and mucous membranes, as well as mucus and enzymes, that physically destroy and/or remove pathogens and debris from areas of the body where they might cause harm or infection. Other examples of physical barriers include tears, acidity in the urine and reproductive tracts, and sebum (the protective oil secreted through hair follicles onto the skin). [2]
Internal Defenses
Internal defenses are also referred to as the body’s second line of defense. These work to protect the body if a pathogen gets past the physical barriers and into the body. Examples of internal defenses include phagocytosis, inflammatory response, and fever. [3]
Phagocytosis
Phagocytosis (făg-ō-sī-TŌ-sĭs) refers to the process of cells engulfing and destroying pathogens (i.e., “cells eating”).  Macrophages “eat up” damaged cells, pathogens, and debris. Another type of white blood cell called neutrophils are also called phagocytes, but as they “clean up,” they become toxic and die, creating pus. Neutrophils are typically the first cells on site to a new infection. [4] See Figure 11.4 [5] for an image of phagocytosis.
Inflammatory Response
Inflammation (in-flă-MĀ-shŏn) is characterized by heat, redness, pain, and swelling. Although inflammation is often perceived as a negative consequence of injury or disease, it is an important process that recruits immune defenses to eliminate pathogens, remove damaged and dead cells, and initiate repair mechanisms. [6]
During the inflammatory response (ĭn-FLĂM-ă-tŏr-ē ri-SPONS), the damaged cells release chemicals, including histamine (HIS-tă-mēn). These chemicals cause redness, heat, and increased permeability of blood vessels so fluid leaks into tissues, causing swelling. These chemicals also attract phagocytes and lymphocytes. [7] See Figure 11.5 [8] for an image of inflammation.
Fever
Fever (FĒ-vŏr), also referred to as pyrexia, is part of the inflammatory response that extends beyond the site of infection and affects the entire body, resulting in an overall increase in body temperature. Health care providers generally consider a fever to be 100.4°F (38°C) or higher.  The rise in body temperature also inhibits the growth of many pathogens. [9]
View the following supplementary YouTube video [10] on nonspecific innate immunity: Immune System, Part 1: Crash Course Anatomy & Physiology #45
Adaptive Immune Response
The adaptive immune response (ă-dăp-tĭv ĭ-mūn rĭ-spŏns) is activated when the nonspecific, innate immune response is insufficient to control an infection. The adaptive immune response requires the body’s exposure to a pathogen to recognize it as a threat in order for it to respond. Exposure can be through direct contact or via immunization. After the adaptive immune system has been exposed to a pathogen, it develops memory cells to recognize this pathogen in the future and quickly mount a defense. [11]
A lymphocyte (LIM-fō-sīt), a specific type of white blood cell, plays a key role in the adaptive immune response. There are two main groups of lymphocytes called B cells and T cells, both of which are formed in bone marrow (bōn MAR-ō). B cells mature in the bone marrow, and T cells mature in the thymus, the rationale for being called “B” cells and “T” cells. B cells are involved in humoral immunity (i.e., immune functions in the blood and other fluids in the body), and T cells are involved in cell-mediated defenses (i.e., fighting invaders within cells). [12]
Humoral Immunity: B cells
Humoral immunity (HYŌŌ-mŏr-ăl ĭ-mū-nĭ-tē) refers to the function of B cells and their production of antibodies. B cells originate and develop in the bone marrow and then migrate in body fluids through the lymph nodes, spleen, and blood to seek out and destroy pathogens in the interstitial spaces. B cells make plasma cells that produce Y-shaped proteins called antibodies (ANT-i-bod-ēz) that destroy pathogens based on their antigens. Antigens (ĂN-tĭ-jĕnz) are markers that tell the immune system whether something in the body is harmful or not. Antigens are found on viruses, bacteria, cancer cells, and even normal cells of the body. Each antigen has a unique shape that the immune system reads like a nametag to know whether or not it belongs in that person’s body. Antibodies are very specific to the antigens they recognize and destroy. They fit onto the antigen like a key to a lock. [13]
When a B cell finds an abnormal cell with an antigen that it has antibodies for, it binds to it and responds by cloning itself into many B cells and differentiating into plasma cells, which release thousands of antibodies per second to attack the pathogen. Some B cells become memory B cells that are involved in immunological memory to ensure a stronger and faster antibody response if the body is exposed to the same antigen in the future.
View the following supplementary YouTube video [14] on adaptive immunity: Immune System, Part 2: Crash Course Anatomy & Physiology #46
Passive Immunity
Passive immunity (PĂS-ĭv im-Ū-nĭt-ē) is a type of immunity obtained by receiving antibodies produced by someone else. For example, infants have passive immunity because they are born with antibodies they received through the placenta from their mother. However, these antibodies are unable to create effector cells or memory cells, so it won’t remember an antigen if it gets infected again. These antibodies disappear between 6 and 12 months of age. Breast milk also contains antibodies, so babies who are breastfed have passive immunity for a longer period of time. [15]
Passive immunization can also be transferred via an injection of antibodies formed by another person or animal. There are five classes of antibodies comprised of the following immunoglobulins: IgG, IgM, IgA, IgD, and IgE. Immunoglobulins provide immediate protection against an antigen, but do not provide long-lasting protection. For example, Hepatitis B Immune Globulin (HBIG) is administered to individuals who have been exposed to hepatitis B as passive immunization to help fight the infection. [16]
Cell-Mediated Response: T cells
When nonspecific, innate immunity and humoral immunity are not effective in defending against pathogens or abnormal cells, the body responds with a cell-mediated response (Sĕl-mēd-ē-āt-ed rĭ-spŏns) using lymphocyte T cells to destroy the abnormal cells. There are two major types of T cells called helper T cells and killer T cells [17] :
- Helper T cells use chemical messengers to activate the adaptive immune response. They stimulate B cells to make antibodies and help develop the killer T cells.
- Killer T cells, also called natural killer (NK) cells or cytotoxic cells, directly kill cells that have been invaded by a virus or are otherwise abnormal. They also clone themselves into many effector T cells and create memory T cells for immunological memory of the antigen.
See Figure 11.6 [18] for a comparison of the function of B cells and cytotoxic T cells. The purple cell is an invading virus. The B cells release antibodies to fight the virus and protect the body’s cells from being invaded by the virus. The cytotoxic T cells recognize body cells that have been infected by the virus and destroy them.
Chemical messaging occurs during the immune response and includes cytokines. Cytokines (SĪ-tō-kīnz) are proteins secreted by cells that act as chemical messengers in immune responses. When a pathogen enters the body, the first immune cell to notice the pathogen is like the conductor of an orchestra. That cell directs all the other immune cells by creating and sending out messages (cytokines) to the rest of the organs or cells in the body to respond to and initiate inflammation. [19]
See Figure 11.7 [20] for an illustration of innate immunity and specific adaptive immunity using an example of a pathogen entering the body through the nose.
View the following YouTube video [21] on cell-mediated immune response: Immune System, Part 3: Crash Course Anatomy & Physiology #47
Immunological Memory
Immunological memory (im-yŭ-NOL-ŏ-jē- kăl MEM-ŏ-rē) refers to the ability of the adaptive immune response to mount a stronger and faster immune response upon reexposure to a pathogen. Memory B and T cells for each specific pathogen are created that provide long-term protection from reinfection with that pathogen. On reexposure, these memory cells facilitate an efficient and quick immune response. For example, when an individual recovers from chicken pox, the body develops a memory of the varicella-zoster virus that will specifically protect it from reinfection if exposed to the virus again. [22]
Acquired immunity refers to immunity that develops with exposure to various antigens as an individual’s immune system builds a defense. However, pathogens can mutate and change the shape of their antigens so the immune system can no longer recognize or defend against it. [23] For example, influenza viruses mutate frequently, requiring annual influenza vaccination.
Immunization
Immunization (ĭm-yū-nĭ-zā-shŏn) is a method to trigger an individual’s acquired immune response and prevent future disease. A vaccine is an agent administered by injection, orally, or by nasal spray that provides active acquired immunity to a particular infectious disease. Small doses of a viral antigen are given to activate immunological memory. Memory cells allow the body to react quickly if exposed to the recognized antigen and efficiently defend against the virus. [24]
Stress and the Immune System
Hormones released during the stress response (also known as the “fight or flight” response by the sympathetic nervous system) include epinephrine, cortisol, and corticosteroids. These hormones suppress T cell immune response, which can result in a weakened immune system. Additionally, long-term stress is associated with an increase in stress-related diseases like hypertension and coronary artery disease. [25]
The Immune Response and Cancer
There are three stages of the immune response to many malignancies [26] :
- Elimination (ĭ-lĭm-ĭ-nā-shŏn) occurs when the immune response first develops antibodies toward tumor-specific antigens and actively kills most cancer cells.
- Equilibrium (ē-kwĭ-lĭb-rē-ŭm) is the period that follows elimination when remaining cancer cells are held in check.
- Escape (ĕs-kāp) from the immune response occurs because many cancers mutate and no longer express specific antigens for which the immune system responds.
- This work is a derivative of Health Alterations by Open RN and is licensed under CC BY 4.0 ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2023. Immune response; [reviewed 2022, Jan 23; cited 2023, Nov 7). https://medlineplus.gov/ency/article/000821.htm ↵
- “ phagocytes.png ” by zzzi zeth is licensed in the Public Domain. ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- “ Tickbite_Inflammation_2482a.jpg ” by Túrelio is licensed under CC BY-SA 3.0-de ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- CrashCourse. (2015, December 8). Immune system, Part 1: Crash Course Anatomy & Physiology #45 [Video]. YouTube. All rights reserved. https://youtu.be/GIJK3dwCWCw?si=YFX4Rpb4U8a_dyPS ↵
- This work is a derivative of Health Alterations by Open RN and is licensed under CC BY 4.0 ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- Cleveland Clinic. (2022, August 16). Antigen . my.clevelandclinic.org/health/diseases/24067-antigen ↵
- CrashCourse. (2015, December 8). Immune system, Part 2: Crash Course Anatomy & Physiology #46 [Video]. YouTube. All rights reserved. https://youtu.be/2DFN4IBZ3rI?feature=shared ↵
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2023. Immune response; [reviewed 2022, Jan 23; cited 2023, Nov 7). https://medlineplus.gov/ency/article/000821.htm ↵
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2023. Immune response. https://medlineplus.gov/ency/article/000821.htm ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- “General_Effector_Mechanisms_of_B_and_T_Cells.png” by סתו כסלו is licensed under CC BY-SA 4.0 ↵
- This work is a derivative of Anatomy and Physiology by OpenStax licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- “2211_Cooperation_Between_Innate_and_Immune_Responses.jpg” by OpenStax is licensed under CC BY 3.0 ↵
- CrashCourse. (2015, December 21). Immune system, Part 3: Crash Course Anatomy & Physiology #47 [Video]. YouTube. All rights reserved. https://youtu.be/rd2cf5hValM?si=sd_XWq6Mn2Sm_Kt1 ↵
- This work is a derivative of Nursing Fundamentals by Open RN and is licensed under CC BY 4.0 ↵
- Cleveland Clinic. (2022, August 16). Antigen . my.clevelandclinic.org/health/diseases/24067-antigen ↵
- A.D.A.M. Medical Encyclopedia [Internet]. Atlanta (GA): A.D.A.M., Inc.; c1997-2023. Immune response; [reviewed 2022, Jan 23; cited 2023, Nov 7). https://medlineplus.gov/ency/article/000821.htm ↵
- This work is a derivative of Anatomy & Physiology by OpenStax and is licensed under CC BY 4.0. Access for free at https://openstax.org/details/books/anatomy-and-physiology-2e ↵
- This work is a derivative of Anatomy & Physiology by OpenStax and is licensed under CC BY 4.0. Access for free at https://openstax.org/details/books/anatomy-and-physiology-2e ↵


11.4: Circular Motion- Linear and Angular Speed
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Radian measure and arc length can be applied to the study of circular motion . In physics the average speed of an object is defined as:
\[ \text{average speed} ~=~ \frac{\text{distance traveled}}{\text{time elapsed}}
\nonumber \]
So suppose that an object moves along a circle of radius \(r \), traveling a distance \(s \) over a period of time \(t \), as in Figure 4.4.1. Then it makes sense to define the (average) linear speed \(\nu \) of the object as:
\[ \nu ~=~ \frac{s}{t}\label{eqn:linspeed} \]
Let \(\theta \) be the angle swept out by the object in that period of time. Then we define the (average) angular speed \(\omega \) of the object as:
\[ \omega ~=~ \frac{\theta}{t}\label{eqn:angspeed} \]
Angular speed gives the rate at which the central angle swept out by the object changes as the object moves around the circle, and it is thus measured in radians per unit time. Linear speed is measured in distance units per unit time (e.g. feet per second). The word linear is used because straightening out the arc traveled by the object along the circle results in a line of the same length, so that the usual definition of speed as distance over time can be used. We will usually omit the word average when discussing linear and angular speed here.
Since the length \(s \) of the arc cut off by a central angle \(\theta \) in a circle of radius \(r \) is \(s=r\,\theta \), we see that
\[ \nu ~=~ \frac{s}{t} ~=~ \frac{r\,\theta}{t} ~=~ \frac{\theta}{t} \;\cdot\; r ~,
\nonumber \]
so that we get the following relation between linear and angular speed:
\[ \nu ~=~ \omega\,r\label{eqn:linang} \]
Example 4.14
An object sweeps out a central angle of \(\frac{\pi}{3} \) radians in \(0.5 \) seconds as it moves along a circle of radius \(3 \) m. Find its linear and angular speed over that time period.
Solution:
Here we have \(t=0.5 \) sec, \(r=3 \) m, and \(\theta = \frac{\pi}{3} \) rad. So the angular speed \(\omega \) is
\[ \omega ~=~ \frac{\theta}{t} ~=~ \frac{\dfrac{\pi}{3}~\text{rad}}{0.5~\text{sec}}
\quad\Rightarrow\quad \boxed{\omega ~=~ \frac{2\pi}{3}~\text{rad/sec}} ~,
\nonumber \]
and thus the linear speed \(\nu \) is
\[ \nu ~=~ \omega\,r ~=~ \left( \frac{2\pi}{3}~\text{rad/sec} \right) \,(3~\text{m})
\quad\Rightarrow\quad \boxed{\nu ~=~ 2\pi~\text{m/sec}} ~.
\nonumber \] Note that the units for \(\omega \) are rad/sec and the units of \(\nu \) are m/sec. Recall that radians are actually unitless, which is why in the Equation \(\nu=\omega\,r \) the radian units disappear.
Example 4.15
An object travels a distance of \(35 \) ft in \(2.7 \) seconds as it moves along a circle of radius \(2 \) ft. Find its linear and angular speed over that time period.
Solution:
Here we have \(t=2.7 \) sec, \(r=2 \) ft, and \(s=35 \) ft. So the linear speed \(\nu \) is
\[ \nu ~=~ \frac{s}{t} ~=~ \frac{35~\text{feet}}{2.7~\text{sec}} \quad\Rightarrow\quad
\boxed{\nu ~=~ 12.96~\text{ft/sec}} ~,
\nonumber \]
and thus the angular speed \(\omega \) is given by
\[ \nonumber
\nu ~=~ \omega\,r \quad\Rightarrow\quad 12.96~\text{ft/sec} ~=~ \omega\,(2~\text{ft})
\quad\Rightarrow\quad \boxed{\omega ~=~ 6.48~\text{rad/sec}} ~.
\nonumber \]
Example 4.16
An object moves at a constant linear speed of \(10 \) m/sec around a circle of radius \(4 \) m. How large of a central angle does it sweep out in \(3.1 \) seconds?
Solution:
Here we have \(t=3.1 \) sec, \(\nu=10 \) m/sec, and \(r=4 \) m. Thus, the angle \(\theta \) is given by
\[ s ~=~ r\,\theta \quad\Rightarrow\quad \theta ~=~ \frac{s}{r} ~=~ \frac{\nu\,t}{r} ~=~
\frac{(10~\text{m/sec})\,(3.1~\text{sec})}{4~\text{m}} ~=~ \boxed{7.75~\text{rad}} ~.
\nonumber \]
In many physical applications angular speed is given in revolutions per minute , abbreviated as rpm. To convert from rpm to, say, radians per second, notice that since there are \(2\pi \) radians in one revolution and \(60 \) seconds in one minute, we can convert \(N \) rpm to radians per second by "canceling the units'' as follows:
\[\require{cancel} \nonumber
N~\text{rpm} ~=~ N~\frac{\cancel{\text{rev}}}{\cancel{\text{min}}} \;\cdot\;
\frac{2\pi~\text{rad}}{1~\cancel{\text{rev}}}
\;\cdot\; \frac{1~\cancel{\text{min}}}{60~\text{sec}} ~=~ \frac{N \cdot 2\pi}{60}~\text{rad/sec}
\nonumber \]
This works because all we did was multiply by \(1 \) twice. Converting to other units for angular speed works in a similar way. Going in the opposite direction, say, from rad/sec to rpm, gives:
\[ N~\text{rad/sec} ~=~ \frac{N \cdot 60}{2\pi}~\text{rpm}
\nonumber \]
Example 4.17
A gear with an outer radius of \(r_1 = 5 \) cm moves in the clockwise direction, causing an interlocking gear with an outer radius of \(r_2 = 4 \) cm to move in the counterclockwise direction at an angular speed of \(\omega_2 = 25 \) rpm. What is the angular speed \(\omega_1 \) of the larger gear?
Figure 4.4.2
Solution:
Imagine a particle on the outer radius of each gear. After the gears have rotated for a period of time \(t>0 \), the circular displacement of each particle will be the same. In other words, \(s_1 = s_2 \), where \(s_1 \) and \(s_2 \) are the distances traveled by the particles on the gears with radii \(r_1 \) and \(r_2 \), respectively.
But \(s_1 = \nu_1 \,t \) and \(s_2 = \nu_2 \,t \), where \(\nu_1 \) and \(\nu_2 \) are the linear speeds of the gears with radii \(r_1 \) and \(r_2 \), respectively. Thus,
\[ \nu_1 \,t = \nu_2 \,t \quad\Rightarrow\quad \nu_1 = \nu_2 ~,
\nonumber \]
so by Equation \ref{eqn:linang} we get the fundamental relation between the two gears:
\[
\boxed{\omega_1 \,r_1 ~=~ \omega_2 \,r_2}\label{eqn:gears}
\nonumber \]
Note that this holds for any two gears. So in our case, we have
\[ \omega_1 \,(5) ~=~ (25) \,(4) \quad\Rightarrow\quad \boxed{\omega_1 ~=~ 20~\text{rpm}} ~.
\nonumber \]


3.2.3: Civil vs. Criminal Liability
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A legal case can be civil or criminal. Each case has different components and requirements. Before one can understand the civil and criminal systems, it is important to understand the aspects of both civil and criminal laws. The scope, consequences, and treatments of each vary.
Constitutional Rights
It is important to understand the Constitution, which is the basis of all law. States are allowed to create and categorize crimes and punishment, as long as they do not violate rights protected by the U.S. Constitution. For example, in a fairly recent United States Supreme Court case, Lawrence v. Texas, the defendants asserted the unconstitutionality of a Texas law (enacted by the Texas legislature) regarding a particular act. When the United States Supreme Court ruled it unconstitutional, Texas could no longer enforce it.
Frequent issues litigated in the courts are:
- Whether evidence must be suppressed (not allowed to be introduced at trial) because it was obtained pursuant to an unreasonable search and seizure (violating the Fourth Amendment). This category might involve a sub-issue about whether officers had sufficient probable cause to conduct a warrantless search. Without a warrant, and without the suspect’s consent, officers generally may only conduct searches if they have “probable cause” to do so; any evidence obtained without consent or probable cause can be objected to, and ultimately ruled inadmissible by the court in trial, if illegally obtained.
- Whether evidence must be suppressed because it was obtained while the suspect was “in custody” without advising a suspect of his rights to remain silent, to speak to an attorney, and to the appointment of an attorney if he cannot afford one (Fifth Amendment privilege against self-incrimination and Sixth Amendment right to counsel), as required by the Supreme Court in the famous Miranda v. Arizona case. The term often used to describe these rights is “Mirandizing,” which is named after the case.
- Whether a state law or constitutional provision provides more protection than the U.S. Constitution.
Components of Crime
There are usually two components to criminal conduct that must be proven by the prosecutor. The prosecutor prosecutes the case against the accused: mens rea (the criminal, or guilty, or “wrongful” mind) and actus reus (the criminal, or guilty, or “wrongful” act).
Each statute creating a crime is supposed to include a description of:
- the mental state ( mens rea ) required to establish that the suspect committed the crime, coupled with
- a description of the conduct ( actus reus ) that the suspect must have done.
The statute generally also indicates the category of crime (felony/misdemeanor/gross misdemeanor).
Criminal Procedures
Generally, the first pleading filed by the prosecutor is called the information . (This step could be described as the criminal counterpart to a civil “complaint.”)
The next stage is called the arraignment , where the defendant appears in court so that the court can determine or confirm his or her identity, inform the defendant of the charge the prosecutor has filed against him or her, and hear the defendant’s plea.
Then, there will be discovery and trial. In criminal cases, the jury will convict only if convinced “beyond a reasonable doubt” that the defendant committed the crime, and the verdict must be unanimous. This type of case involves a higher burden of proof than in civil cases.
Criminal and Civil Law
Criminal law addresses behaviors that are offenses against the public, society, or state. Examples of criminal law offenses include assault, drunk driving, and theft. In contrast, civil laws address behavior that causes an injury to the private rights of individuals in areas such as child support, divorce, contracts, property, and the person. Examples of civil law offenses include libel, slander, or contract breaches.
Criminal and civil cases differ in who initiates the case, how the case is decided, what punishments or penalties are issued, requirements of proof, and legal protections provided.
Initiation and Roles
Criminal and civil cases are initiated differently, and the titles of the individuals involved differ slightly. Criminal cases are only initiated by the federal or state government in response to a law being broken. The federal or state governments are known as the prosecution. The prosecution is an attorney, or group of attorneys, hired by the government to present a case against the accused. Criminal cases are usually titled something like “State v. [last name of the defendant accused of a crime].” In criminal prosecutions, the victim is not a party to the lawsuit, but might be a witness for the state at the trial.
In contrast, private parties initiate civil cases when they feel that someone has injured them. Again, civil cases stem from breach of contract, custody cases, and attacks on one’s character. Private parties can include an individual, a group, or a business. The person, group, or business who initiates the case is referred to as the plaintiff or complainant. The accused is referred to as the defendant, in both criminal and civil proceedings.
Typically, there is a difference in the burden of proof for the two types of cases. In a criminal case, the defendant must be proven guilty “beyond a reasonable doubt.” In a civil case, the defendant must be proven liable through a “preponderance of the evidence.” In other words, the prosecution in a civil case must prove that it is more probable than not that the defendant is liable.
In criminal cases, the defendant is entitled to an attorney and may be appointed an attorney if he or she is not able to afford one. The state appoints the attorney. In contrast, all parties involved in a civil case are required to secure their own legal representation.
Typically, civil and criminal laws use different terminology, and being found guilty or accountable in each type of case results in different consequences.
In a civil action (lawsuit), the plaintiff is the person who is alleging that he or she has actually been harmed (physically, financially, or in another manner), and the defendant is the one who is asked to pay damages or otherwise compensate the plaintiff. Outside of financial compensation, the plaintiff may be ordered to do something or refrain from doing something, which is referred to as injunctive relief.
In the Liebeck v. McDonald’s case, a woman sued McDonald’s for serving hot coffee. The woman spilled hot coffee on her lap while trying to add cream and sugar. The woman sued McDonald’s for negligence in a civil suit. The issue centered on whether or not the coffee’s specific temperature was unreasonably hot. McDonald’s lost the lawsuit. The compensatory verdict was \(\$160,000\). McDonald’s was found liable.
Conversely, if a defendant is convicted of committing a crime, the consequences are usually incarceration (jail/prison) and/or a fine (payment of money to the state).
The word used to describe the legal responsibility for harm in a civil case is liability, not guilt. Guilty is the word used to describe a person found guilty of committing a crime in a criminal case.
Businesses can be charged with criminal acts as well. In 2017, Oliver Schmidt, former manager of a Volkswagen engineering office near Detroit, was arrested. He faced years in prison for attempts to defraud the United States, wire fraud, violation of the Clean Air Act, and a charge of giving an untrue statement under the Clean Air Act. Schmidt’s actions directly violated a business law and, since his actions violated an established law, he was held criminally liable. In December of 2017, Schmidt was sentenced to seven years in prison.
Professional Negligence
Professional negligence is often called malpractice . A professional’s duty of care is usually a duty to exercise the degree of care, skill, diligence, and knowledge commonly possessed and exercised by a reasonable, careful, and prudent professional of the same type in the state (or sometimes in the community). Along with attorneys and health care providers, the following professionals might be sued for malpractice: accountants, architects, engineers, surveyors, insurance brokers, real estate agents and brokers, and clergy.
For negligence, the usual kind of damages recoverable are compensatory , or money to compensate for the injuries/damages incurred to make the person whole (e.g., money for medical bills, lost wages, loss of future earning capacity, pain and suffering, emotional distress, property damage, etc.).
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3.6: Navigating Google Docs
By the end of this section, you will be able to:
- Describe the major features of Google Docs
- Understand how to create a Google Doc in Google Drive
WorldCorp uses both Microsoft Office and Google Docs to conduct its daily business activities. These activities are with both internal and external groups. For example, you might be sharing confidential sales data with the internal marketing department at WorldCorp, but also share a version of the same information with less data to external vendors. Both programs offer advantages: Microsoft has decades of being the industry standard in word processing, spreadsheets, and presentation software, while Google offers a user-friendly design and collaborative features.
In this section, you will revisit your market trends report, using Docs instead of Microsoft Word to create it. You will see how Docs is different from Word and how to use it to your advantage.
Menus
What tabs are to Word, menus are to Docs. In Word, the tools we use to prepare documents are arranged in tabs and then in command groups within those tabs. In Docs, the tools are arranged in menus instead of tabs. There are some similarities between the names of the menus and tabs: For example, you have the Insert tab in Word and the Insert menu in Docs. Docs also has a nice, user-friendly feature in which the tools that are used more frequently, such as some of the alignment tools and the font tools, are on a toolbar under the menu. This toolbar is called the action bar , and it is a static menu bar; it doesn’t change, like Word’s ribbon. This keeps those tools handy so that it is faster and easier for the user to change items in the document. Many of the tools on the action bar are similar to what you will find on the Home tab in Word. The menus in Google were covered in more detail in the Essentials of Software Applications for Business chapter, which discussed the essentials of the Google programs.
Edit Menu
This menu is similar to the Edit menu in Word. Looking at Figure 3.36, you can see that this menu has commands such as Select All, Undo, Redo, and Find and Replace. As in Word, the keyboard shortcut Ctrl+Z will undo the last action you took, while Ctrl+Y is the opposite: It redoes what you have undone with Ctrl+Z.
On a Mac, these commands are Command+Z and Command+Y , respectively. Any time a Ctrl+ function is used on a Windows computer, the corresponding function key on a Mac will be the Command key.
Paste without formatting is a useful tool for copying and pasting text only, without any of the source formatting (such as font, font size, or color). This is particularly helpful when copying and pasting from an email or website.
View Menu
The View menu contains tools for looking at your document in different ways. It lets you see the file in three different modes: editing, suggesting, and reading. It also gives the user options for things to toggle on and off, such as the ruler and section breaks. The document outline found in the View menu (Show outline) is similar to the Navigation pane outline view in Word (Figure 3.37). Showing the equation toolbar will let you add math notation. Show section breaks allows the user to see where their document sections begin and end. Lastly, the Full screen view is a view of the document that increases the window size to fit your whole screen (you won’t see the Windows Start menu or your toolbar), and the window borders are seamless.
Insert Menu
The Insert menu has many tools and features that are available in Word, yet in Word, these commands are distributed throughout different tabs. Inserting images, graphs, or tables works the same way in Docs as in Word, but inserting drawings is unique to Docs. With Docs, you can choose to insert a drawing and either make a drawing on the spot, or insert a drawing that is already saved in Google Drive.
From the Insert menu, you can also add conventional document features such as footnotes, headers, page breaks, bookmarks, and special characters (Figure 3.38). There is also a way to insert math equations using the Equation command. You will find some differences between the programs and how they deal with such features.
Format Menu
The Format menu shown in Figure 3.39 is the source for formatting text, paragraphs, indents, line spacing, columns, and lists. The page’s headers and footers, numbers, and horizontal or vertical canvas are also formatted here. As with Word, the user needs to select the text area that they want to change, and then select the tool needed to modify it. Additionally, tables that were inserted using the tools in the Insert menu can be further stylized to a professional look using the formatting tools available here, such as adjusting cell shading, cell borders, and font.
Tools Menu
The Tools menu has some interesting features that Word doesn’t have, such as the Explore command . The Explore command is a unique feature in the Google suite of programs that uses machine learning to offer suggestions and predict what information you might need as you are creating files. For example, the Explore command lets you search the web for the citations you have but need to complete, or references that you don’t have and want to find. It can also suggest other Docs and Sheets that you own or are shared on that may be referenced or connected to your current document. The Explore command can also suggest images that might be connected to what you are currently working on. These images can be from your files or from images on the web. Both citations and references will be formatted in the manual of style of your choice—APA or MLA, for instance. The tools for checking spelling and grammar and word count function in a similar way to Word. You will learn more about the Explore command in Collaborative Editing and Reviewing in Google Docs.
Docs also contains a tool for tracking changes, similar to Word’s Track Changes. This tool, available through a drop-down menu in the top right of the document window, allows the user to choose between Editing (normal editing of your own document), Suggesting (tracking your changes), and Viewing (view-only), as shown in Figure 3.40.
Through the Tools menu (Figure 3.41), you can choose Review suggested edits, which allows you to view the suggested edits one by one and choose whether you’d like to accept or reject them. The Tools menu also contains the Preferences window, which offers some of the general settings for your documents, such as whether to use Smart Quotes and autocapitalization. (In Word, the Preferences are contained in the File menu, which is covered in the chapter on Essentials of Software Applications for Business.
Creating a Doc
We are going to begin by creating our market trends report, starting with industry analysis information. The most direct way to create a new Doc is to log in to your Google Drive. Once you are in the Drive, you can create a new Doc by selecting the New plus sign, as discussed in the chapter on Essentials of Software Applications for Business. Then, choose Google Docs from the list. This will automatically open a new window with a blank document. You could also hover over the arrow to the right of the Google Docs icon and choose Blank document or From a template to create the new file. As an alternative, once in your Drive, you can create a new document by selecting the Google Apps icon, as Figure 3.42 shows. This will open a drop-down menu, and you will choose which app to access, in this case that would be Docs for the Google word processor application. A new tab will appear in your browser with the Docs. Here, you can choose to open from recent documents or create a new document either by a template or an entirely new file (by choosing blank).
If you select the first icon, Blank, Docs will open a blank canvas, similar to how Word opens its blank documents. You can also create a new document using a template. There are many kinds of default templates in Docs’s Template Gallery, including résumés, letters, project proposals, work notes, brochures, newsletters, legal agreements, and several educational document templates (like essays, reports, class notes, and lesson plans).


9.2: Activities
Equipment
- aluminum bar
- support assemblies, one with a pulley
- hanging weights & string
- rubber band
- paperclips
- plumb-bob
- ruler
- goniometer (adjustable protractor)
The General Idea
We will use methods of solving static equilibrium problems to indirectly measure forces present in a system of stationary objects. The system in question looks like this:
The lab consists of two parts:
- You are allowed to adjust the amount of variable weight however you see fit. With this power, and armed only with a plumb-bob, determine the mass of the uniform rod. You should also vary the weights by very small amounts (amounts that don't change the system's state a noticeable amount) as a means of determining the uncertainty in your answer.
-
Reassemble the system with an amount of hanging weight that is
substantially different
from the weight you used in part 1. Then, armed with only a plumb-bob and a goniometer, do the following:
- Re-compute the mass of the rod using this setup. Confirm that the value you compute falls within the boundaries of uncertainty of the answer you got in part 1.
- Compute the force exerted on the rod by the rubber band. Devise a way to check your answer another way that doesn't involve static equilibrium methods (you may disassemble the system). There is no uncertainty check for this part of the lab, but you should compute by what percentage the two answers differ (if it is more than 5%, you have almost certainly made an error, as you should be able to get close to 1%).
Some Things to Think About
This lab is very straightforward in its statement, so there is not a lot to say about it, but here are a couple of things that you should know already:
- If you are not drawing free-body diagrams, choosing a coordinate system and a pivot point, breaking forces into components – basically treating this like a physics homework problem – then you are missing the point entirely.
- Make sure you are measuring angles properly with the goniometer – the vertex of the angle has to coincide with the goniometer's pivot, and the two lines that form the angle lie along the central lines in the arms of the goniometer.
Lab Report
Craft a lab report for these activities and analysis, making sure to include every contributing group member's name on the front page. You are strongly encouraged to refer back to the Read Me as you do this, to make sure that you are not leaving out anything important. You should also feel free to get feedback from your lab TA whenever you find that your group requires clarification or is at an impasse.
Every member of the group must upload a separate digital copy of the report to their lab assignment in Canvas prior to leaving the lab classroom . These reports are not to be written outside the lab setting.


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3.4: Basic Accounting Principles
Learning Outcomes
- Identify the major underlying accounting principles of consistency, full disclosure, materiality, verifiability and conservatism
What is the Consistency Principle?
The consistency principle states that, once you adopt an accounting principle or method, continue to follow it consistently in future accounting periods so that the results reported from period to period are comparable. However, companies can change an accounting principle or method if the new version in some way improves the usefulness of the reported financial results. For instance, GAAP allows for several different ways of valuing inventory (goods held for sale in the ordinary course of business.)
During the first nine months of fiscal 2008, Home Depot implemented a new enterprise resource planning (“ERP”) system, including a new inventory system, for its retail operations in Canada and changed its method of accounting for inventory for its retail operations in Canada from the lower of cost (first-in, first-out) or market, as determined by the retail inventory method, to the lower of cost or market using a weighted-average cost method. This was disclosed, as required by GAAP, in the footnotes to the audited financial statements.
What is Full Disclosure?
The full disclosure principle states that you should include in an entity’s financial statements all information that would affect a reader’s understanding of those statements, such as changes in accounting principles applied. The interpretation of this principle is highly judgmental, since the amount of information that can be provided is potentially massive. To reduce the amount of disclosure, it is customary to only disclose information about events that are likely to have a material impact on the entity’s financial position or financial results. In fact, the full disclosure concept is not usually followed for internally-generated financial statements, where management may only want to read the “bare bones” financial statements.
What is the Materiality Concept?
The materiality principle states that an accounting standard can be ignored if the net impact of doing so has such a small impact on the financial statements that a reader of the financial statements would not be misled. Under generally accepted accounting principles (GAAP), you do not have to implement the provisions of an accounting standard if an item is immaterial. This definition does not provide definitive guidance in distinguishing material information from immaterial information, so it is necessary to exercise judgment in deciding if a transaction is material.
The Securities and Exchange Commission has suggested for presentation purposes that an item representing at least 5% of total assets should be separately disclosed in the balance sheet. However, much smaller items may be considered material. For example, if a minor item would have changed a net profit to a net loss, that item could be considered material, no matter how small it might be. Similarly, a transaction would be considered material if its inclusion in the financial statements would change a ratio sufficiently to bring an entity out of compliance with its lender covenants.
As an example of a clearly immaterial item, you may have prepaid $100 of rent on a post office box that covers the next six months; under the matching principle, you should charge the rent to expense over six months. However, the amount of the expense is so small that no reader of the financial statements will be misled if you charge the entire $100 to expense in the current period, rather than spreading it over the usage period. In fact, if the financial statements are rounded to the nearest thousand or million dollars, this transaction would not alter the financial statements at all.
The materiality concept varies based on the size of the entity. A massive multi-national company may consider a $1 million transaction to be immaterial in proportion to its total activity, but $1 million could exceed the revenues of a small local firm, and so would be very material for that smaller company.
The materiality principle is especially important when deciding whether a transaction should be recorded as part of the closing process, since eliminating some transactions can significantly reduce the amount of time required to issue financial statements. It is useful to discuss with the company’s auditors what constitutes a material item, so that there will be no issues with these items when the financial statements are audited.
What is the Principle of Verifiability?
A company’s accounting results are verifiable when they’re reproducible, so that, given the same data and assumptions, an independent accountant would come up with the same result the company did. Verifiably is the cumulative effect of using historical cost, objectivity, and the monetary unit principle.
Cost Principle
Under GAAP in the U.S., assets are recorded and reported on the balance sheet at their original cost. Although some assets may be overstated, and some, like land, may actually be understated in terms of their actual fair market value, the FASB has determined that reporting assets at their historical cost serves the combined principles of consistency (from firm to firm and from year to year), objectivity, and conservatism. Historical cost is objective because an auditor, or anyone for that matter, could observe the receipt for the asset and come up with the same cost, which is, in fact, one of the tests that auditors perform on major assets.
Suppose a firm purchases land for $20,000 and a building for $100,000. The combined asset reported on the balance sheet would be $120,000, and any accountant or accounting firm asked to record or verify this amount would come up with the same number, even if one person thought the land might be worth $60,000 and another hired an appraiser to estimate a fair market value of only $10,000. Outside opinions don’t matter in the world of historical cost.
Under International Financial Reporting Standards (IFRS), the company would be allowed to restate and report the land at fair market value, if that could be established with any certainty (usually by comparing the asset to current sales of similar assets.) This is one of the major differences between IFRS and GAAP. The FASB justifies using historical cost under the standard of objectivity.
Objectivity
The objectivity principle is the concept that the financial statements of an organization are based on solid evidence. This is what got Enron into trouble. The CEO and CFO were basing revenues and asset values on opinions and guesses, it turned out. The auditors were not objective in their assessment of the financial statements, presumably because they were under pressure from the consulting side of the business (Arthur Anderson.) The principles at the firm wanted to keep the multi-million dollar contract with Enron, causing them to be less than independent in their audit.
By using an objective viewpoint when constructing financial statements, the result should be financial information that investors can rely upon when evaluating the financial results, cash flows, and financial position of an entity.
The Monetary Unit Principle
The monetary unit principle states that you only record business transactions that can be expressed in terms of a currency and assumes that the value of that currency remains relatively stable over time. When you are reading a U.S. GAAP prepared financial statement, looking at inventory, for instance, you know you are looking at a dollar figure, not a number of physical units.
What is Conservatism?
The conservatism principle says if there is doubt between two alternatives, the accountant should opt for the one that reports a lesser asset amount or a greater liability amount, and a lesser amount of net income. Thus, when given a choice between several outcomes where the probabilities of occurrence are equally likely, you should recognize that transaction resulting in the lower amount of profit, or at least the deferral of a profit. Similarly, if a choice of outcomes with similar probabilities of occurrence will impact the value of an asset, recognize the transaction resulting in a lower recorded asset valuation.
Under the conservatism principle, if there is uncertainty about incurring a loss, you should tend toward recording the loss. Conversely, if there is uncertainty about recording a gain, you should not record the gain.
The conservatism principle is the foundation for the lower of cost or market rule, which states that you should record inventory at the lower of either its acquisition cost or its current market value.
Practice Questions


5.2: Compound Interest
Most banks, loans, and credit cards charge compound interest , not simple interest. Compound interest is both calculated on the original principal and on all interest that has been added to the original principal. You can think of this as "interest on your interest."
Compound interest is interest that is paid or earned on the principal as well as on the interest that has accrued.
Interest can be compounded at various time intervals. Interest on a mortgage or auto loan is usually compounded monthly. Interest on a savings account may be compounded quarterly (four times a year). Interest on a credit card may be compounded weekly or even daily. Here are some common compounding types that you may encounter in financial problems and in your everyday life.
| Compounding type | Number of compounding periods per year |
|---|---|
| Annually | 1 |
| Semiannually | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
Consider the following example that illustrates how interest is compounded.
We deposit $1,000 in a bank account offering 3% interest compounded monthly. Let's explore how our money will grow.
Solution
The \(3\%\) interest rate is an annual percentage rate (APR) – the total interest rate to be paid during the year. Because interest is being paid monthly, we will earn only \(\frac{3 \%}{12}=0.25 \% = 0.0025\) per month.
- In the first month, \(P=$1,000\) and \(r=0.0025\), so
\(I=$1,000(0.0025)=$2.50\)
\(F=$1,000+$2.50=$1,002.50\)
At the end of the first month, we will earn $2.50 in interest, raising our account balance to $1,002.50.
- In the second month, \(P=$1,002.50\) and \(r=0.0025\), so
\(I=$1,002.50(0.0025)=$2.51 \; \) (rounded)
\(F=$1,002.50+ $2.51=$1,005.51\)
Notice that at the end of the second month we will earn slightly more interest than in the first month. This is because we earned interest not only on the original $1,000 principal, but we also earned interest on the $2.50 of interest accumulated during the first month. This is the key advantage that compounding of interest gives us.
The table shows how the interest accumulates and is compounded for a complete year (12 months):
| Month | Starting Balance | Interest Earned | Ending Balance |
|---|---|---|---|
| 1 | $1,000.00 | $1,000.00 \(\times\) 0.0025 = $2.50 | $1,000.00 + $2.50 = $1,002.50 |
| 2 | $1,002.50 | $1,002.50 \(\times\) 0.0025 = $2.51 | $1,002.50 + $2.51 = $1,005.01 |
| 3 | $1,005.01 | $1,005.01 \(\times\) 0.0025 = $2.51 | $1,005.01 + $2.51 = $1,007.52 |
| 4 | $1,007.52 | $1,007.52 \(\times\) 0.0025 = $2.52 | $1,007.52 + $2.52 = $1,010.04 |
| 5 | $1,010.04 | $1,010.05 \(\times\) 0.0025 = $2.53 | $1,010.05 + $2.53 = $1,012.57 |
| 6 | $1,012.57 | $1,012.57 \(\times\) 0.0025 = $2.53 | $1,012.57 + $2.53 = $1,015.10 |
| 7 | $1,015.10 | $1,015.10 \(\times\) 0.0025 = $2.54 | $1,015.10 + $2.54 = $1,017.64 |
| 8 | $1,017.64 | $1,017.64 \(\times\) 0.0025 = $2.54 | $1,017.64 + $2.54 = $1,020.18 |
| 9 | $1,020.18 | $1,020.18 \(\times\) 0.0025 = $2.55 | $1,020.18 + $2.55 = $1,022.73 |
| 10 | $1,022.73 | $1,022.73 \(\times\) 0.0025 = $2.56 | $1,022.73 + $2.56 = $1,025.29 |
| 11 | $1,025.29 | $1,025.29 \(\times\) 0.0025 = $2.56 | $1,025.29 + $2.56 = $1,027.85 |
| 12 | $1,027.85 | $1,027.85\(\times\) 0.0025 = $2.57 | $1,027.85 + $2.57 = $1,030.42 |
So, after one year of compounding the interest monthly, the balance in the account is $1,030.42.
The calculations of interest and the new balance month-after-month can get tedious and long. To make these calculations more efficient, observe the pattern in the table: The future value after \(m\) months, \(F_{m}\), can be presented using the future value from the previous month, \(F_{m-1}\):
\(F_{m}=F_{m-1}\cdot(1 + \frac{0.03}{12}) \)
This observation leads to the standard compound interest formula.
\(F=P\left(1+\frac{r}{n}\right)^{nt}\)
where,
- F is future value
- P is present value, or principal
- r is the annual percentage rate (APR) written as a decimal
- n is the number of compounding periods per year
- t is number of years
Using the formula derived above, let's solve Example 1 again where \(P=$1,000\), \(r=0.03 \text{ annually}\), \(n=12 \text{ times}\), and \(t = 1 \text{ year}\). A screenshot of entering the calculation on a TI calculator is also shown.
\(F=1,000\left(1+\frac{0.03}{12}\right)^{12 \cdot 1}\)
The accumulated balance after 12 months is $1,030.42 and agrees with the result in the table.
So is there a significant difference between compounded interest and simple interest? The next example will investigate this question.
A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a higher interest rate than a savings or checking account, but you cannot access your investment for a specified length of time. Suppose you deposit $3,000 into a CD paying 6% interest compounded monthly. After 20 years, how will the value of the CD compare to the value of another type of account that pays 6% simple interest?
Solution
In this example,
\(\begin{array} {ll} P=\$ 3,000 & \text{the initial deposit} \\ r = 0.06 & 6\% \text{ annual rate} \\ n = 12 & \text{12 months in 1 year} \\ t = 20 & \text{since we’re looking for how much we’ll have after 20 years} \end{array}\)
The table and graph compares an account's balance using 6% simple interest to the CD balance using 6% interest compounded monthly every 5 years throughout 35 years.
\(\begin{array}{|c|c|c|}
\hline \text { Years } & \begin{array}{c}
\text { Value of Account Paying 6% Simple Interest } \\
\text { (\$15 per month) } \\
\end{array} & \begin{array}{c}
\text { Value of CD Paying } 6 \% \text { Interest Compounded Monthly } \\ (0.5 \% \text { per month})
\end{array} \\ \hline 5 & \$ 3,900 & \$ 4,046.55 \\
\hline 10 & \$ 4,800 & \$ 5,458.19 \\
\hline 15 & \$ 5,700 & \$ 7,362.28 \\
\hline 20 & \$ 6,600 & \$ 9,930.61 \\
\hline 25 & \$ 7,500 & \$ 13,394.91 \\
\hline 30 & \$ 8,400 & \$ 18,067.73 \\
\hline 35 & \$ 9,300 & \$ 24,370.65 \\
\hline
\end{array}\)
The graph shows there is not a great deal of difference between the two types of interest in the first few years. But as time increases, the value of the CD where interest is compounded increases at a faster and faster pace and at a much faster rate than the value of the account paying simple interest.
Using the formulas for simple interest and compound interest, we can find the future value \(F\) of the two different accounts in \(t=20 \text { years}\) with an initial deposit of \(P=$3,000\) and an interest rate of \(r=6 \%\).
Simple Interest: \(F=P(1+rt)= 3,000(1+0.06 \cdot 20) = $6,660\)
Compounded Interest: \(F=P\left(1+\frac{r}{n}\right)^{nt}=3,000\left(1+\frac{0.06}{12}\right)^{12 \cdot 20} = $9,930.61\)
When interest is compounded, the amount of money in the CD is \($9,930.61 - $6,600.00 = $3,330.61 \;\) more than if simple interest had accrued.
One can always use any scientific calculator to find value of \(F\) using the compound interest formula. However, computations become much more algebraically intense when solving for the principal \(P\), for the rate \(r\), or for the time \(t\). Therefore, it is recommended to use the Time Value Money Solver (TVM Solver) app available on a TI calculator to solve all problems related to compounded interest.
To access the TVM Solver , press the APPS key and then choose Finance... .
Let us consider how to use the TVM Solver settings on following example.
Find the total amount accumulated and the total interest earned if $4,000 is invested for 2 years at a 6% compounded monthly.
Solution
When solving for a value using the TVM Solver app, you will need to enter all the given values, but skip over the value you are solving for (in this case \(FV\).) Once you have entered all given values, go back to the value you want to find and press the ALPHA button and then ENTER . A square will appear next to \(FV\) to show that this value was calculated using the given information.
According to the TVM Solver , the total amount in the account will accumulate to $4,508.64. This means that the account has earned \($4,508.64 - $4,000 = $508.64 \; \) in interest during the 2 years.
For the following examples, we will continue to make use of the TVM Solver .
Find the total amount accumulated and the total interest earned when $2,000 is invested for 4 years at 5% interest compounded quarterly (four times each year.)
Solution
For this scenario,
- \(N = 16\): The number of times the interest is compounded is \(4 \text { years } \times 4 \text { times per year } = 16\).
- \(I\% = 5\): Remember to leave this as a percentage. Do not change to a decimal.
- \(PV = -2000\): Recall that \('-'\) represents money leaving you and put into an account.
Completing the remaining values as in Example 3, we then solve for future value \(FV\) by moving the cursor back to the value for \(FV\) and pressing ALPHA and then ENTER. The result is shown on the calculator screen.
The accumulated amount in the account will be \($2,439.78. \) The total interest earned during the 2 years will be \($2,439.78 – $2,000.00 = $439.78\).
Use the TVM Solver app to solve:
Find the total amount accumulated and the total interest earned when $2,500 is invested for 3 years at 4% interest compounded semi-annually (twice a year).
How much do you need to invest into a 5-year CD (certificate of deposit) that pays 3% interest compounded monthly so that it will be worth $5,000 at the end of the term?
Solution
In this problem, the future value is given, \(FV = $5,000\), and we need to solve for the present value, \(PV\). We also are given that \(N = 5 \text{ years } \times 12 \text { times per year }= 60 \text { times}\) and \(I = 3 \%\).
As the TVM Solver calculates, you need to invest $4,304.35 in order to reach $5,000 in 5 years.
A rare violin has an estimated value of $12,000. Its value history indicates that it appreciates at 14% per year. How many years will it take to appreciate to $60,000?
In summary, the TVM Solver app on the TI calculator is similar to the financial math functions in Microsoft Excel . Using the TVM Solver application for compound interest problems allows us to solve for any parameter (\(PV\), \(FV\), \(I\), \(N\), and so on) without having to solve a logarithmic or exponential equation. While the TVM Solver is useful for solving compound interest problems, it is not useful for solving simple interest problems.
The next two sections will use the TVM Solver app to solve annuity and loan repayment problems.