Question 1

What is the effective annual rate of 6.5 percent compounded quarterly?

Accepted Answer

EAR = [1 + (0.065/4)] ⁴ - 1 = 6.66 percent

Question 2

Your aunt loaned you money at 1.00 percent interest per month.What is the APR of this loan?

Accepted Answer

APR = 1.00 × 12 = 12 percent

Question 3

PayDay Loans is offering a special on one-year loans.The company will loan you $5,000 today in exchange for one payment of $5,900 one year from now.What is the APR on this loan?

Accepted Answer

FV = $5,900 = $5,000 × (1 + APR)¹; APR = 18 percent

Question 4

The Men's Warehouse charges 1.6 percent interest per month.What rate of interest are its credit customers actually paying?

Accepted Answer

EAR = (1 + 0.016)¹² - 1 = 20.98 percent

Question 5

A loan that compounds interest monthly has an EAR of 14.40 percent.What is the APR?

Accepted Answer

EAR = 0.1440 = [1 + (APR/12)]¹² - 1; APR = 13.53 percent

Question 6

Belk Department Store charges a daily rate of 0.01 percent on its store credit cards.What interest rate is the company required by law to report to potential customers?

Accepted Answer

APR = 0.01 percent × 365 = 36.50 percent

Question 7

Amish Bakery needs $210,000 today to fund a new project.The project will not produce any cash flows for two years and thus the firm agreed to a two-year,pure discount loan at 7.5 percent interest.How much will the firm owe on this loan at the time it must be repaid?

Accepted Answer

FV = $210,000 × (1 + 0.075)² = $242,681.25

Question 8

A credit card has a stated interest rate of 14.56 percent.What is the APR if interest is compounded monthly?

Accepted Answer

The stated rate is the APR.

Question 9

First Trust offers personal loans at 7.7 percent compounded monthly.Second Bank offers similar loans at 7.75 percent compounded semiannually.Which one of the following statements is correct concerning these loans?

Accepted Answer

EAR _{First Trust} = [1 + (0.077/12)]¹² - 1 = 7.98 percent; EAR _{Second Bank} = [1 + (0.075/2)]² - 1 = 7.90 percent

Question 10

Hometown Builders is borrowing $150,000 today for five years.The loan is an interest-only loan with an APR of 8.5 percent.Payments are to be made annually.What is the amount of the first annual payment?

Accepted Answer

Payment _{Year 1} = $150,000 × 0.085 = $12,750

Question 11

Today,you are borrowing $13,800 to purchase a car.What will be your monthly payment amount if the loan is for four years at 7.5 percent interest?

Accepted Answer

To calculate the monthly payments for a loan, we can use the following formula:

Monthly Payment = (P × r) / (1 – (1 + r)^-n)

Where P is the principal amount (loan amount), r is the monthly interest rate (annual interest rate divided by 12), and n is the total number of months for the loan (number of years multiplied by 12).

In this case, P = $13,800, r = 7.5% / 12 = 0.00625, and n = 4 × 12 = 48.

Plugging these values into the formula, we get:

Monthly Payment = (13,800 × 0.00625) / (1 – (1 + 0.00625)^-48) = $333.67

Therefore, the monthly payment amount for a four-year loan at 7.5% interest for $13,800 would be $333.67. The best choice is C.

Question 12

A new financial services company just opened in your town.To attract customers,it is offering a "9-11" loan special.The company will lend $9 today in exchange for a payment of $11 one year from today.What is the APR on this loan?

Accepted Answer

FV = $9 × (1 + r)¹ = $11; r = 22.22 percent

Question 13

The Townhouse Galleries offers credit to its customers at a rate of 1.6 percent per month.What is the effective annual rate of this credit offer?

Accepted Answer

EAR = (1 + 0.016)¹² - 1 = 20.98 percent

Question 14

Radio Shack offers credit to its customers and charges interest of 1.2 percent per month.What is the annual percentage rate?

Accepted Answer

APR = 1.2 percent × 12 = 14.40 percent

Question 15

What is the effective annual rate of 14.9 percent compounded quarterly?

Accepted Answer

EAR = [1 + (0.149/4)]⁴ - 1 = 15.75 percent

Question 16

What is the effective annual rate of 10 percent compounded semiannually?

Accepted Answer

EAR = [1 + (0.10/2)]² - 1 = 10.25 percent

Question 17

Popeye's Fried Chicken just took out an 8 percent interest-only loan of $50,000 for three years.Payments are to be made at the end of each year.What is the amount of the payment that will be due at the end of year 3?

Accepted Answer

Payment _{Year 3} = $50,000 + ($50,000 × 0.08) = $54,000

Question 18

Today,you are borrowing money from your local bank.The loan is to be repaid in one lump sum payment of $15,000 one year from now.How much money are you borrowing today if the APR is 10.6 percent?

Accepted Answer

We can use the formula for future value of a single sum: 
FV = PV(1 + r)^n 
where FV is the future value, PV is the present value (what we're trying to find), r is the annual interest rate (in decimal form), and n is the number of years.

Substituting the given values: 
$15,000 = PV(1 + 0.106)^1

$15,000 = PV(1.106)

PV = $15,000 / 1.106

PV = $13,562.39

So the amount of money borrowed today is $13,562.39. Therefore, the best choice is C.

Question 19

The Rent-to-Own Store has a six-year,interest-only loan at 12 percent interest.The firm originally borrowed $125,000.How much will the firm pay in total interest over the life of the loan?

Accepted Answer

Total interest = $125,000 × 0.12 × 6 = $90,000

Question 20

You have an outstanding loan with an EAR of 14.6 percent.What is the APR if interest is compounded monthly?

Accepted Answer

To convert EAR to APR compounded monthly, use the formula:
APR = [(1 + EAR/monthly)^12 - 1] x 100

Substituting the given values, we get:
APR = [(1 + 0.146/12)^12 - 1] x 100
APR = 13.71%

Therefore, the answer is choice B.

Quiz 5: Discounted Cash Flow Valuation