Question

Question #18: You just graduated and want to give yourself a gift of a new automobile. The terms of the deal are as follow:

• Cost of the new automobile is $32,600 • You will pay $1,800 to reduce the cost of the automobile • The interest rate of the loan is 4.80%, compounded monthly • The term of the loan is 5 years Required:

Calculate the monthly payment.

Answer 1

Answer)

Calculation of monthly payment

Installments are to be paid monthly

Amount Borrowed	$ 30,800
Annual Rate of interest	4.80%
Compounding	Monthly
Number of months	60 Months

Calculation of amount of installments:

Amount of installment = [A X R X (1 + R) ^N]/ [(1 + R) ^N-1]

Where,

A = amount borrowed,

R = effective annual rate of return

N = number of periods

Amount of installment = [$ 30,800 X 0.004 X (1 + 0.004) ^60]/ [(1 + 0.004) ^60-1]

                                           = [$ 30,800 X 0.004 X 1.27064072]/ [1.27064072-1]

                                          = $ 156.5429/0.27064072

                                         = $ 578.42 or $ 578 (Approximately)

Therefore the amount of monthly payment will be $ 578.

Note: Since the payment is being made on monthly basis, the effective rate of interest will be annual rate of interest divided by 12 and the effective number of periods will be number of years multiplied by 12.

Working Note:

Calculation of amount of loan

Amount of loan = Cost of Automobile – down payment

                              = $ 32,600 – $ 1,800

                              = $ 30,800