Question 1

Billingsley, Inc. is borrowing $60,000 for 5 years at an APR of 8 percent. The principal is to be repaid in equal annual payments over the life of the loan with interest paid annually. Payments will be made at the end of each year. What is the total payment due for year 3 of this loan?

Accepted Answer

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Question 2

What does it mean when a loan is amortized? Explain how amortization methods can vary from one loan to another.

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Question 3

Taylor Farms is borrowing $75,000 for 3 years at an APR of 9 percent. The loan calls for the principal balance to be reduced by equal amounts over the life of the loan. Interest is to be paid in full each year. The payments are to be made annually at the end of each year. How much will Taylor Farms pay in interest over the life of this loan?

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Question 4

Webster Bank is offering 2.8 percent compounded daily on its savings accounts. If you deposit $2,500 today, how much will you have in the account in 15 years?

Accepted Answer

Using the formula for compound interest, we have: 
A = P(1 + r/n)^(nt), where 
A = amount after 15 years 
P = initial deposit = $2,500 
r = annual interest rate = 2.8% 
n = number of times interest is compounded per year = 365 (daily) 
t = number of years = 15

Plugging in the values, we get: 
A = 2500(1 + 0.028/365)^(365*15) 
= $3,804.84

Therefore, the best choice is D.

Question 5

Friendly Credit Corp. wants to earn an effective annual return on its consumer loans of 13 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers?

Accepted Answer

Since the bank uses daily compounding, the annual percentage rate (APR) will be higher than the effective annual return. Using the formula APR = [(1 + r/n)^n - 1] x 100%, where r is the effective annual return and n is the number of compounding periods per year, we can solve for the APR: 
APR = [(1 + 0.13/365)^365 - 1] x 100% = 12.22% 
Therefore, the bank is required by law to report an APR of 12.22% to potential borrowers, even though it earns an effective annual return of 13%.

Question 6

Identify 4 ways that you can use annuity computations in your everyday life.

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Question 7

Wesson Metals has an outstanding loan that calls for equal annual payments of $9,768.46 over the life of the loan. The original loan amount was $50,000 at an APR of 8.5 percent. How much of the second loan payment is interest?

Accepted Answer

First, we need to find the number of payments over the life of the loan:

n = 30 (since there are 30 years in the life of the loan)

Next, we can use the loan payment formula to find the amount that goes towards interest in the second loan payment:

Payment = (PMT) = $9,768.46

Interest rate per period = (APR) / (number of payments per year) = 8.5% / 12 = 0.70833%

Balance = (PV) = $50,000

Number of periods = (n) = 30

Using these values, we can solve for the amount of interest in the second loan payment:

Interest = Payment * [(1 - (1 + interest rate per period)^(-number of periods)) / interest rate per period] - (Balance * (1 + interest rate per period)^(-number of periods))

Plugging in the values:

Interest = $9,768.46 * [(1 - (1 + 0.70833%)^(-30)) / 0.70833%] - ($50,000 * (1 + 0.70833%)^(-30))

Interest = $3,780.93

Therefore, the answer is B.

Question 8

You want to borrow $36,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $750, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan?

Accepted Answer

Using the loan formula, we can solve for the APR:

Loan amount = Payment x ((1-(1+r/12)^-n)/(r/12))

where r is the APR and n is the number of payments

Plugging in the given values:

$36,000 = $750 x ((1-(1+r/12)^-60)/(r/12))

To solve for r, we can use trial and error or Excel's Goal Seek function. The highest rate that can be afforded with monthly payments of $750 is 9.15 percent. Therefore, the answer is D.

Question 9

If the appropriate discount rate for the following cash flows is 11.7 percent per year, what is the present value of the cash flows?

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Question 10

You want to buy a new sports coupe for $84,600, and the finance office at the dealership has quoted you a 7.1 percent APR loan for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

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Question 11

You have just purchased a new warehouse. To finance the purchase, you've arranged for a 25-year mortgage for 80 percent of the $1,800,000 purchase price. The monthly payment on this loan will be $10,800. What is the APR? The EAR?

Accepted Answer

Loan amount = 0.80 × $1,800,000 = $1,440,000 EAR = [1 + (0.076687/12)]¹² - 1 = 7.94 percent

Question 12

Julie is borrowing $12,800 to purchase a car. The loan terms are 36 months at 7.5 percent interest. How much interest will she pay on this loan if she pays the loan as agreed? Round your answer to the nearest whole dollar.

Accepted Answer

Total interest paid = ($398.16 × 36) - $12,800 = $1,534 (rounded)

Question 13

Consider an ordinary annuity and the variables that are related to that annuity. For each of the following sets of variables, identify whether the relationship between the two variables is direct (D) or inverse (I). Assume all other variables are held constant.

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Question 14

Eastern Shore Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $10,000 per year forever. If the required return on this investment is 5.5 percent, how much will you pay for the policy?

Accepted Answer

We can use the perpetuity formula to calculate the value of the investment policy:

PV = Payment / Required Return

PV = $10,000 / 0.055

PV = $181,818.18

Therefore, the amount you would pay for the policy is $181,818.18, which is closest to option B.

Question 15

You want to buy a new sports car from Roy's Cars for $51,800. The contract is in the form of a 48-month annuity due at a 9.2 percent APR. What will your monthly payment be?

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Question 16

Jesse just won the state lottery. He has been given the option of receiving either $66.4 million today or $5 million a year for the next 30 years, with the first payment paid today. Describe the process that Jesse should use to determine which payment option he prefers. Ignore all taxes and assume that Jesse will live for at least 45 more years.

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Question 17

Explain the similarities and differences among an ordinary annuity, an annuity due, and a perpetuity.

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Question 18

The Egg House just borrowed $260,000 to build a new restaurant. The loan terms call for equal annual payments at the end of each year. The loan is for 15 years at an APR of 8 percent. How much of the first annual payment will be used to reduce the principal balance?

Accepted Answer

To find the equal annual payments, we can use the formula for the present value of an annuity:

PV = PMT × (1 – (1 + r)-n) / r

where PV is the loan amount, PMT is the annual payment, r is the annual interest rate (APR divided by the number of compounding periods per year), and n is the total number of payments (15).

Substituting the given values, we get:

260,000 = PMT × (1 – (1 + 0.08/1)-15) / (0.08/1)
PMT = $30,625.54

So, the Egg House will make annual payments of $30,625.54 for 15 years.

To find how much of the first annual payment will be used to reduce the principal balance (i.e. the loan amount), we can use the loan amortization formula:

Principal Payment = PMT – (Balance × r)

where Balance is the remaining loan balance, which starts at the original loan amount and decreases by the amount of each principal payment.

In the first year, the Balance is 260,000, so:

Principal Payment = 30,625.54 – (260,000 × 0.08/1) = $9,575.68

Therefore, Choice B is the correct answer.

Question 19

If you put up $46,000 today in exchange for a 6.75 percent 15-year annuity, what will the annual cash flow be?

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Question 20

Appalachian Bank offers you a $135,000, 9-year term loan at 7.5 percent annual interest. What will your annual loan payment be?

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Quiz 5: Discounted Cash Flow Valuation