Question

Suppose that under the Plan of Repayment one should pay off the debt in a number of equal​ end-of-month installments​ (principal and​ interest). This is the customary way to pay off loans on​ automobiles, house​ mortgages, etc. A friend of yours has financed ​$29,000 on the purchase of a new​ automobile, and the annual interest rate is 6​% (0.50% per​ month).

a. Monthly payments over a 60​-month loan period will be how​ much?

b. How much interest and principal will be paid within three month of this​ loan?

Answer 1

(a) Monthly payment ($) = Loan amount / P/A(0.5%, 60) = 29,000 / 51.7256** = 560.65

(b) Loan amortization schedule for first 3 months is as follows. Note that

(i) Interest payment in month N = Beginning balance in month N x 0.005

(ii) Principal payment in month N = $560.65 - Interest payment in month N

Month	Beginning balance ($)	Monthly Payment ($)	Interest Payment ($)	Principal Payment ($)	Ending Balance ($)
1	1,50,000.00	560.65	62.50	498.15	1,49,439.35
2	1,49,439.35	560.65	62.27	498.38	1,48,878.70
3	1,48,878.70	560.65	62.03	498.62	1,48,318.05
TOTAL			186.80	1,495.15

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.5%, 60) = [1 - (1.005)^-60] / 0.005 = (1 - 0.7414) / 0.005 = 0.2586 / 0.005 = 51.7256