Question

Suppose you borrowed $32,000 for 4 years with quarterly payments at an APR of 6%. What is the quarterly payment? (ordinary annuity)

PLEASE SHOW WORK USING FORMULAS *NOT through excel or financial calulator

Amortize the first four payments. Use the table below:

(Payment number) (Payment) (Interest) (Prinicipal) (Remaining Balance)

1 _______ _______ _______ ________

2 _______ _______ ________ ________

3 _______ _______ _______ _________

4 _______ ________ _______ __________

How much in interest will you pay over the life of the loan? _____

Answer 1

We can use the present value of annuity formula to calculate the quarterly loan payment amount.
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = Loan amount = $32000
P = Quarterly loan payment = ?
r = rate of interest per quarter = 6%/4 = 0.015
n = no.of quarters = 4 years * 4 = 16
32000 = P * {[1 - (1+0.015)^-16]/0.015}
32000 = P * 14.13126
P = 2264.48
Quarterly Loan payment = $2264.48
Amortize the first four payments.
Payment number	Payment	Interest	Principal	Remaining balance
1	$2,264.48	$480.00	$1,784.48	$30,215.52
2	$2,264.48	$453.23	$1,811.25	$28,404.27
3	$2,264.48	$426.06	$1,838.42	$26,565.86
4	$2,264.48	$398.49	$1,865.99	$24,699.86
Interest paid over the life of the loan = [Quarterly loan payment * no.of quarterly payments] - Original Loan amount
Interest paid over the life of the loan = [$2264.48 * 16] - $32000 = $4,231.72