Question

How much will you owe a bank at the end of the 27th month if you took a loan of $25,000 for a period of 72 months at a rate of 9% per year compounded monthly, if you paid the bank your entire bonus of $9,000 at the end of the 12th month to bring down the loan quickly? You make payments to the bank at the end of every month.

$7,090

$11,063

$421

$3,727

Answer 1

Answer is $7,090

We can construct an amortization table and solve it.

Month	Opening Loan Balance	Principal Part	Interest Part	Installment	Closing Loan Balance
1	25,000	263	188	451	24,737
2	24,737	265	186	451	24,472
3	24,472	267	184	451	24,205
4	24,205	269	182	451	23,936
5	23,936	271	180	451	23,664
6	23,664	273	177	451	23,391
7	23,391	275	175	451	23,116
8	23,116	277	173	451	22,839
9	22,839	279	171	451	22,559
10	22,559	281	169	451	22,278
11	22,278	284	167	451	21,994
12	21,994	9,286	165	9,451	12,709
13	12,709	355	95	451	12,353
14	12,353	358	93	451	11,995
15	11,995	361	90	451	11,635
16	11,635	363	87	451	11,271
17	11,271	366	85	451	10,905
18	10,905	369	82	451	10,536
19	10,536	372	79	451	10,165
20	10,165	374	76	451	9,790
21	9,790	377	73	451	9,413
22	9,413	380	71	451	9,033
23	9,033	383	68	451	8,650
24	8,650	386	65	451	8,265
25	8,265	389	62	451	7,876
26	7,876	392	59	451	7,484
27	7,484	395	56	451	7,090
28	7,090	397	53	451	6,692
29	6,692	400	50	451	6,292
30	6,292	403	47	451	5,888
31	5,888	406	44	451	5,482
32	5,482	410	41	451	5,072
33	5,072	413	38	451	4,660
34	4,660	416	35	451	4,244
35	4,244	419	32	451	3,825
36	3,825	422	29	451	3,403
37	3,403	425	26	451	2,978
38	2,978	428	22	451	2,550
39	2,550	432	19	451	2,118
40	2,118	435	16	451	1,684
41	1,684	438	13	451	1,246
42	1,246	441	9	451	804
43	804	445	6	451	360
44	360	360	3	363	-

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