Question

General Appliances (GA) offers you the following financing terms for a new washer and dryer with a price tag of $2,489: You make a down payment of $250 now and 36 consecutive monthly installments of $75 (the first payment is due in one month). What is the effective annual interest rate (EAR) implied in GA’s financing option? Note: To solve this problem use, for example, Goal Seek in Excel.

Select one:

a. 1.05%

b. 12.6%

c. 13.3%

d. 5.5%

e. 0.45%

f. 10.8%

g. 16.1%

h. 10.0%

NOTE: Please show all the work, without using EXCEL (Step by step with equations) Thanks!

Answer 1

We can use the present value of annuity formula to derive the effective annual interest rate (EAR) implied in GA’s financing option.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = Price of washer and dryer - down payment = $2489 - $250 = $2239
P = monthly installment = $75
r = monthly interest rate = ?
n = number of months payment = 36
2239 = 75*{[1 - (1+r)^-36]/r}
29.85333 = [1 - (1+r)^-36]/r
r = 0.0105
Monthly Interest rate = 1.05%
Effective annual interest rate (EAR) implied in GA’s financing option = 1.05% * 12 = 12.6%
The answer is Option b.