Question 1

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?

Accepted Answer

The answer of You want to buy a new sports...

Question 2

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

Accepted Answer

The answer of Appalachian Bank offers you a $135,000,nine-year term...

Question 3

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

Accepted Answer

The answer of What does it mean when a loan...

Question 4

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

Principal payment = $30,375.68 - ($260,000 × 0.08) = $9,575.68

Question 5

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 6

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

Accepted Answer

The annual cash flow of an annuity can be calculated using the formula for the present value of an annuity: PV = C * [(1 - (1 + r)^-n) / r]. Solving for C (the annual cash flow), we get C = PV / [(1 - (1 + r)^-n) / r]. Plugging in the values: PV = $46,000, r = 6.75% or 0.0675, and n = 15, we find that C is approximately $4,971.10.

Question 7

Alfa 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 4.75 percent,how much will you pay for the policy?

Accepted Answer

PV = $10,000/0.0475 = $210,526.32

Question 8

Compass Bank is offering 0.8 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

FV = $2,500 × [1 + (0.008/365)]¹⁵ ^{× 365} = $2,818.74

Question 9

Given an interest rate of 5.85 percent per year,what is the value at year t = 8 of a perpetual stream of $2,500 payments that begin at year t = 25?

Accepted Answer

PV _{t = 24} = $2,500/0.0585 = $42,735.04; PV _{t = 8} = $42,735.04/(1 + 0.0585)¹⁶ = $17,208.00

Question 10

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 11

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?

Accepted Answer

= $78,270.77

Question 12

PayDay Loans wants to earn an effective annual return on its consumer loans of 18 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

0.18 = [1 + (APR/365)³⁶⁵ - 1; APR = 16.56 percent

Question 13

If today is year 0,what is the future value of the following cash flows 10 years from now? Assume an interest rate of 7.8 percent per year.

Accepted Answer

FV _{Year 10} = [$8,500 × (1 + 0.078)⁸] + [$9,300 × (1 + 0.078)⁷] + [$7,100 × (1 + 0.078)⁴] = $40,822.55

Question 14

You want to borrow $40,000 from your local bank to buy a new sailboat.You can afford to make monthly payments of $775,but no more.Assuming monthly compounding,what is the highest rate you can afford on a 60-month APR loan?

Accepted Answer

Using the formula for finding the monthly payment on a loan with monthly compounding:
P = (r(PV))/1-(1+r)^-n
where P is the monthly payment, r is the monthly interest rate, PV is the present value or loan amount, and n is the number of payments.

Plugging in the given values:
PV = $40,000
P = $775
n = 60 months

Solving for r:
r = 0.005083 or 0.5083%

This is the monthly interest rate. To convert it to an APR or annual percentage rate, we need to multiply it by 12:
APR = 0.060995 or 6.1%

Therefore, the highest rate that meets the monthly payment requirement is 6.1 percent.

Question 15

Billingsley,Inc.is borrowing $60,000 for five 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

The answer of Billingsley,Inc.is borrowing $60,000 for five years at...

Question 16

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?

Accepted Answer

The correct answer is A. The monthly payment for a 48-month annuity due at a 9.2 percent APR is $1,284.13.

Question 17

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

Accepted Answer

The answer of Explain the similarities and differences among an...

Question 18

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

To find out how much of the second payment is interest, we can first calculate the total interest paid over the life of the loan.

Using the loan amount of $50,000 and an APR of 8.5%, we can find the annual interest rate by multiplying the APR by the loan amount:

8.5% x $50,000 = $4,250

This gives us an annual interest payment of $4,250. Since the loan requires equal annual payments, we can divide the total interest by the number of payments:

$4,250 ÷ 5 = $850

So each payment includes $850 in interest. To find the answer, we simply subtract the principal payment from the total payment:

$9,768.46 - $850 = $3,780.93

Therefore, the answer is B.

Question 19

Taylor Farms is borrowing $75,000 for three 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?

Accepted Answer

Total interest = $13,500

Question 20

A 4-year annuity of eight $6,200 semiannual payments will begin 6 years from now,with the first payment coming 6.5 years from now.If the discount rate is 7 percent compounded semiannually,what is the value of this annuity 4 years from now?

Accepted Answer

PV _{Year 4} = $42,618.52/[1 + (0.07/2)]⁴ = $37,139.58

Quiz 5: Discounted Cash Flow Valuation