Question

Maggie Kool buys an air conditioner with $100 down and 35 equal installments of $25. The total purchase price(cash price) is $600. If Maggie pay off the bill after the 23 payment. what rebate is Maggie entitled to and what will be the final payoff?

Answer 1

Solution:

Let imputed rate of interest in installment is i

Purchase price of AC = $600

Down payment = $100

Therefore present value of installment at i interest rate = $600 - $100 = $500

$25 * Cumulative PV factor for 35 periods at i rate = $500

Cumulative PV factor for 35 periods at i rate = 20

Now refer to PV table, the factor 20 at 35 periods come at discount rate of 3.50%

Hence imputed interest rate in installment is 3.50%

Loan Amortization Schedule
Period	Cash Paid	Interest	Carrying value
0			$500
1	$25	$18	$493
2	$25	$17	$485
3	$25	$17	$477
4	$25	$17	$468
5	$25	$16	$460
6	$25	$16	$451
7	$25	$16	$442
8	$25	$15	$432
9	$25	$15	$422
10	$25	$15	$412
11	$25	$14	$401
12	$25	$14	$390
13	$25	$14	$379
14	$25	$13	$367
15	$25	$13	$355
16	$25	$12	$343
17	$25	$12	$330
18	$25	$12	$316
19	$25	$11	$302
20	$25	$11	$288
21	$25	$10	$273
22	$25	$10	$258
23	$25	$9	$242
24	$25	$8	$225
25	$25	$8	$208
26	$25	$7	$190
27	$25	$7	$172
28	$25	$6	$153
29	$25	$5	$133
30	$25	$5	$113
31	$25	$4	$92
32	$25	$3	$70
33	$25	$2	$47
34	$25	$2	$24
35	$25	$1	$0

Carrying value after payment of 23rd installment = $242

Remaining installmetn value after 23 rd payment = $25*12 = $300

Rebate entitled by Maggie = $300 - $242 = $58

Final payoff amount after 23rd installment = $242