Chapter 4, Problem 107P

To determine

Tabular Representation of the balance due, principal payment, and interest rate.

Answer to Problem 107P

The monthly payment is $77.46 and the interest paid in the last month is $0.39.

Explanation of Solution

Given information:

• Loan Amount - $15,000
• Time period − 36 months & 60 months.
• Rate of Interest − 8.9% per annum.

• Capital Recovery Factor:

The capital recovery factor is used to find the uniform annual amount A of a uniform series from a known present worth at the given interest rate i. It is calculated as:

$A=P\left[\frac{i{(1+i)}^n}{{(1+i)}^n-1}\right]=P(A/P,i,n)$.

Calculation:

• For 36 months
The loan amount is $15,000. The monthly payments are to be made, therefore, the rate of interest will be divided by 12

$\begin{array}{l}RoI=(8.9\%)/12=0.741\%\\ MonthlyPayment=P(A/P,i,n)=\$476.30\end{array}$

Months	Total Payment	Principal	Interest Rate	Opening Balance	Closing Balance
1	476.30	365.05	111.25	15000.00	14634.95
2	476.30	367.76	108.54	14634.95	14267.20
3	476.30	370.48	105.82	14267.20	13896.71
4	476.30	373.23	103.07	13896.71	13523.48
5	476.30	376.00	100.30	13523.48	13147.48
6	476.30	378.79	97.51	13147.48	12768.70
7	476.30	381.60	94.70	12768.70	12387.10
8	476.30	384.43	91.87	12387.10	12002.67
9	476.30	387.28	89.02	12002.67	11615.39
10	476.30	390.15	86.15	11615.39	11225.24
11	476.30	393.04	83.25	11225.24	10832.20
12	476.30	395.96	80.34	10832.20	10436.24
13	476.30	398.90	77.40	10436.24	10037.34
14	476.30	401.85	74.44	10037.34	9635.49
15	476.30	404.83	71.46	9635.49	9230.65
16	476.30	407.84	68.46	9230.65	8822.82
17	476.30	410.86	65.44	8822.82	8411.95
18	476.30	413.91	62.39	8411.95	7998.04
19	476.30	416.98	59.32	7998.04	7581.06
20	476.30	420.07	56.23	7581.06	7160.99
21	476.30	423.19	53.11	7160.99	6737.80
22	476.30	426.33	49.97	6737.80	6311.48
23	476.30	429.49	46.81	6311.48	5881.99
24	476.30	432.67	43.62	5881.99	5449.32
25	476.30	435.88	40.42	5449.32	5013.43
26	476.30	439.12	37.18	5013.43	4574.32
27	476.30	442.37	33.93	4574.32	4131.95
28	476.30	445.65	30.65	4131.95	3686.29
29	476.30	448.96	27.34	3686.29	3237.34
30	476.30	452.29	24.01	3237.34	2785.05
31	476.30	455.64	20.66	2785.05	2329.41
32	476.30	459.02	17.28	2329.41	1870.38
33	476.30	462.43	13.87	1870.38	1407.96
34	476.30	465.86	10.44	1407.96	942.10
35	476.30	469.31	6.99	942.10	472.79
36	476.30	472.79	3.51	472.79	0.00

• For 60 months

The loan amount is $15,000. The monthly payments are to be made, therefore, the rate of interest will be divided by 12

$\begin{array}{l}RoI=(8.9\%)/12=0.741\%\\ MonthlyPayment=P(A/P,i,n)=\$310.65\end{array}$

Months	Total Payment	Principal	Interest Rate	Opening Balance	Closing Balance
1	310.65	199.40	111.25	15000.00	14800.60
2	310.65	200.88	109.77	14800.60	14599.73
3	310.65	202.37	108.28	14599.73	14397.36
4	310.65	203.87	106.78	14397.36	14193.49
5	310.65	205.38	105.27	14193.49	13988.11
6	310.65	206.90	103.75	13988.11	13781.21
7	310.65	208.44	102.21	13781.21	13572.77
8	310.65	209.98	100.66	13572.77	13362.79
9	310.65	211.54	99.11	13362.79	13151.25
10	310.65	213.11	97.54	13151.25	12938.14
11	310.65	214.69	95.96	12938.14	12723.45
12	310.65	216.28	94.37	12723.45	12507.17
13	310.65	217.89	92.76	12507.17	12289.28
14	310.65	219.50	91.15	12289.28	12069.78
15	310.65	221.13	89.52	12069.78	11848.65
16	310.65	222.77	87.88	11848.65	11625.88
17	310.65	224.42	86.23	11625.88	11401.46
18	310.65	226.09	84.56	11401.46	11175.37
19	310.65	227.76	82.88	11175.37	10947.60
20	310.65	229.45	81.19	10947.60	10718.15
21	310.65	231.15	79.49	10718.15	10487.00
22	310.65	232.87	77.78	10487.00	10254.13
23	310.65	234.60	76.05	10254.13	10019.53
24	310.65	236.34	74.31	10019.53	9783.19
25	310.65	238.09	72.56	9783.19	9545.10
26	310.65	239.85	70.79	9545.10	9305.25
27	310.65	241.63	69.01	9305.25	9063.62
28	310.65	243.43	67.22	9063.62	8820.19
29	310.65	245.23	65.42	8820.19	8574.96
30	310.65	247.05	63.60	8574.96	8327.91
31	310.65	248.88	61.77	8327.91	8079.03
32	310.65	250.73	59.92	8079.03	7828.30
33	310.65	252.59	58.06	7828.30	7575.71
34	310.65	254.46	56.19	7575.71	7321.25
35	310.65	256.35	54.30	7321.25	7064.90
36	310.65	258.25	52.40	7064.90	6806.65
37	310.65	260.17	50.48	6806.65	6546.48
38	310.65	262.09	48.55	6546.48	6284.39
39	310.65	264.04	46.61	6284.39	6020.35
40	310.65	266.00	44.65	6020.35	5754.35
41	310.65	267.97	42.68	5754.35	5486.38
42	310.65	269.96	40.69	5486.38	5216.43
43	310.65	271.96	38.69	5216.43	4944.47
44	310.65	273.98	36.67	4944.47	4670.49
45	310.65	276.01	34.64	4670.49	4394.48
46	310.65	278.06	32.59	4394.48	4116.43
47	310.65	280.12	30.53	4116.43	3836.31
48	310.65	282.20	28.45	3836.31	3554.12
49	310.65	284.29	26.36	3554.12	3269.83
50	310.65	286.40	24.25	3269.83	2983.43
51	310.65	288.52	22.13	2983.43	2694.91
52	310.65	290.66	19.99	2694.91	2404.25
53	310.65	292.82	17.83	2404.25	2111.43
54	310.65	294.99	15.66	2111.43	1816.44
55	310.65	297.18	13.47	1816.44	1519.27
56	310.65	299.38	11.27	1519.27	1219.89
57	310.65	301.60	9.05	1219.89	918.29
58	310.65	303.84	6.81	918.29	614.45
59	310.65	306.09	4.56	614.45	308.36
60	310.65	308.36	2.29	308.36	0.00