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 ​$20,000 on the purchase of a new​ automobile, and the annual interest rate is 12% (1% per​ month).

a. Monthly payments over a 36​-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(1%, 36) = 20,000 / 30.1075** = 664.29

(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 0.01

(ii) Principal payment in month N = $664.29 - Interest payment in month N

Month	Beginning balance ($)	Monthly Payment ($)	Interest Payment ($)	Principal Payment ($)	Ending Balance ($)
1	20,000.00	664.29	200.00	464.29	19,335.71
2	19,335.71	664.29	193.36	470.93	18,671.42
3	18,671.42	664.29	186.71	477.58	18,007.13
TOTAL			580.07	1,412.80

**From P/A Factor table