Question

A loan of $12,000

is repaid by payments of $571

at the end of every three months. Interest is 9%

compounded quarterly

(a) How many payments are required to repay the debt?

(b) What is the size of the final payment?

Answer 1

Loan amount = Present value of future payments = payment * [1-(1+i)^-n]/i

i = interest rate per period

n = numbber of periods

=>

571 * [1-(1+0.09/4)^-n]/(0.09/4) = 12000

=>

a)

no of payments n = 28.78 periods

b)

using amortization schedule

	Beginning Balance	Interest	Principal	Ending Balance
1	$12,000.00	$270.00	$301.00	$11,699.00
2	$11,699.00	$263.23	$307.77	$11,391.23
3	$11,391.23	$256.30	$314.70	$11,076.54
4	$11,076.54	$249.22	$321.78	$10,754.76
5	$10,754.76	$241.98	$329.02	$10,425.75
6	$10,425.75	$234.58	$336.42	$10,089.33
7	$10,089.33	$227.01	$343.99	$9,745.34
8	$9,745.34	$219.27	$351.73	$9,393.62
9	$9,393.62	$211.36	$359.64	$9,033.98
10	$9,033.98	$203.26	$367.74	$8,666.24
11	$8,666.24	$194.99	$376.01	$8,290.24
12	$8,290.24	$186.53	$384.47	$7,905.77
13	$7,905.77	$177.88	$393.12	$7,512.65
14	$7,512.65	$169.03	$401.97	$7,110.69
15	$7,110.69	$159.99	$411.01	$6,699.68
16	$6,699.68	$150.74	$420.26	$6,279.43
17	$6,279.43	$141.29	$429.71	$5,849.72
18	$5,849.72	$131.62	$439.38	$5,410.34
19	$5,410.34	$121.73	$449.27	$4,961.08
20	$4,961.08	$111.62	$459.38	$4,501.71
21	$4,501.71	$101.29	$469.71	$4,032.00
22	$4,032.00	$90.72	$480.28	$3,551.72
23	$3,551.72	$79.91	$491.09	$3,060.64
24	$3,060.64	$68.86	$502.14	$2,558.50
25	$2,558.50	$57.57	$513.43	$2,045.07
26	$2,045.07	$46.01	$524.99	$1,520.09
27	$1,520.09	$34.20	$536.80	$983.29
28	$983.29	$22.12	$548.88	$434.42
28.78	$434.42	$8.67	$434.42	$0.00

hence size of final payment is 434.42