A certain college graduate, Sallie Evans, has $24,000 in student-loan debt at the end of her college career. The interest rate on this debt is 0.75% per month. If monthly payments on this loan are $432.61, how many months will it take for Sallie to repay the entire loan? (4.6)

Question

Accepted Answer

Here we are given P = $24,000, A = $432.61 per month, and i = 0.75% per month. The equivalence relationship is:
$24, 000 = $432.61 (P/A, 0.75% per month, N) We can determine N by inspecting Table C-3. From Table C-3 when N = 72 months, we see the following:
$432.61(55.4768) = $24, 000.
Thus, the loan will be completely repaid in 72 months.

Table C-3 Discrete Compounding; i = 3.4%
Single Payment			Uniform Series				Uniform Gradient
N	Compound Amount Factor	Present Worth Factor	Compound Amount Factor	Present Worth Factor	Sinking Fund Factor	Capital Recovery Factor	Gradient Present Worth Factor	Gradient Uniform Series Factor	N
	To Find F Given P	To Find P Given F	To Find F Given A	To Find P Given A	To Find A Given F	To Find A Given P	To Find P Given G	To Find A Given G
	F/P	P/F	F/A	P/A	A/F	A/P	P/G	A/G
1	1.0075	0.9926	1	0.9926	1	1.0075	0	0	1
2	1.0151	0.9852	2.0075	1.9777	0.4981	0.5056	0.985	0.4981	2
3	1.0227	0.9778	3.0226	2.9556	0.3308	0.3383	2.941	0.995	3
4	1.0303	0.9706	4.0452	3.9261	0.2472	0.2547	5.853	1.4907	4
5	1.0381	0.9633	5.0756	4.8894	0.197	0.2045	9.706	1.9851	5
6	1.0459	0.9562	6.1136	5.8456	0.1636	0.1711	14.487	2.4782	6
7	1.0537	0.949	7.1595	6.7946	0.1397	0.1472	20.181	2.9701	7
8	1.0616	0.942	8.2132	7.7366	0.1218	0.1293	26.775	3.4608	8
9	1.0696	0.935	9.2748	8.6716	0.1078	0.1153	34.254	3.9502	9
10	1.0776	0.928	10.3443	9.5996	0.0967	0.1042	42.606	4.4384	10
11	1.0857	0.9211	11.4219	10.5207	0.0876	0.0951	51.817	4.9253	11
12	1.0938	0.9142	12.5076	11.4349	0.08	0.0875	61.874	5.411	12
13	1.102	0.9074	13.6014	12.3423	0.0735	0.081	72.763	5.8954	13
14	1.1103	0.9007	14.7034	13.243	0.068	0.0755	84.472	6.3786	14
15	1.1186	0.894	15.8137	14.137	0.0632	0.0707	96.988	6.8606	15
16	1.127	0.8873	16.9323	15.0243	0.0591	0.0666	110.297	7.3413	16
17	1.1354	0.8807	18.0593	15.905	0.0554	0.0629	124.389	7.8207	17
18	1.144	0.8742	19.1947	16.7792	0.0521	0.0596	139.249	8.2989	18
19	1.1525	0.8676	20.3387	17.6468	0.0492	0.0567	154.867	8.7759	19
20	1.1612	0.8612	21.4912	18.508	0.0465	0.054	171.23	9.2516	20
21	1.1699	0.8548	22.6524	19.3628	0.0441	0.0516	188.325	9.7261	21
22	1.1787	0.8484	23.8223	20.2112	0.042	0.0495	206.142	10.1994	22
23	1.1875	0.8421	25.001	21.0533	0.04	0.0475	224.668	10.6714	23
24	1.1964	0.8358	26.1885	21.8891	0.0382	0.0457	243.892	11.1422	24
25	1.2054	0.8296	27.3849	22.7188	0.0365	0.044	263.803	11.6117	25
30	1.2513	0.7992	33.5029	26.7751	0.0298	0.0373	373.263	13.9407	30
36	1.3086	0.7641	41.1527	34.4468	0.0243	0.0318	524.992	16.6946	36
40	1.3483	0.7416	46.4464	34.4469	0.0215	0.029	637.469	18.5058	40
48	1.4314	0.6986	57.5207	40.1848	0.0174	0.0249	886.84	22.0691	48
60	1.5657	0.6387	75.4241	48.1734	0.0133	0.0208	1313.519	27.2665	60
72	1.7126	0.5839	95.007	55.4768	0.0105	0.018	1791.246	32.2882	72
84	1.8732	0.5338	116.4269	62.154	0.0086	0.0161	2308.128	37.1357	84
100	2.1111	0.4737	148.1445	70.1746	0.0068	0.0143	3040.745	43.3311	100
∞				133.3333		0.0075			∞

Question 4.Z: A certain college graduate, Sallie Evans, has $24,000 in stu...

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