Question

You want to buy a new sports coupe for $74,500, and the finance office at the dealership has quoted you a loan with an APR of 6.9 percent for 36 months to buy the car.
Required:
a. What will your monthly payments be?
b. What is the effective annual rate on this loan?

Answer 1

Answer:

a) Monthly payments = $22,969.38

b) Effective rate of return= 7.12%

Explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.

The monthly installment is computed as follows:  

Monthly installment= Loan amount/annuity factor

Loan amount; = 74,500

Annuity factor = (1 - (1+r)^(-n))/r

r -monthly rate of interest, n- number of months

r- 6.9%/12 = 0.575 % = 0.00575, n = 36 =

Annuity factor = ( 1- (1+00575)^(-36)/0.00575= 32.434

Monthly installment = Loan amount /annuity factor

=  74,500/32.434= 22,969.38

Required monthly payments = $22,969.38

Effective annual interest rate

Effective rate of return = ((1+r)^n- 1) × 100

where r - monthly interest rate- 6.9%/12 = 0.575%

n- number of months= 12 months

Effective rate of return - (1+00575)^(12) - 1× 100=  7.12%

Effective rate of return= 7.12%