Question

darcy james borrowed $15,000 which she is paying back in 48 monthly payments of $420 each. with 14 payments remaining, she decides to repay the loan in full. use the rules of 78 to find the amount necessary to pay off the loan

Answer 1

Given - Loan Amount = $15,000, Total Monthly Payments = 48 monthly payments, Installment amount = $420

Calculation as per rule 78 :-

Month	Start Balance	Interest	Principal	End Balance	Cum. Int. Paid	Interest left to Pay
1	15000	210.61	209.39	14790.61	210.61	4949.39
2	14790.61	206.22	213.78	14576.83	416.83	4743.17
3	14576.83	201.84	218.16	14358.67	618.67	4541.33
4	14358.67	197.45	222.55	14136.12	816.12	4343.88
5	14136.12	193.06	226.94	13909.18	1009.18	4150.82
6	13909.18	188.67	231.33	13677.85	1197.85	3962.15
7	13677.85	184.29	235.71	13442.14	1382.14	3777.86
8	13442.14	179.9	240.1	13202.04	1562.04	3597.96
9	13202.04	175.51	244.49	12957.55	1737.55	3422.45
10	12957.55	171.12	248.88	12708.67	1908.67	3251.33
11	12708.67	166.73	253.27	12455.4	2075.4	3084.6
12	12455.4	162.35	257.65	12197.75	2237.75	2922.25
13	12197.75	157.96	262.04	11935.71	2395.71	2764.29
14	11935.71	153.57	266.43	11669.28	2549.28	2610.72
15	11669.28	149.18	270.82	11398.46	2698.46	2461.54
16	11398.46	144.8	275.2	11123.26	2843.26	2316.74
17	11123.26	140.41	279.59	10843.67	2983.67	2176.33
18	10843.67	136.02	283.98	10559.69	3119.69	2040.31
19	10559.69	131.63	288.37	10271.32	3251.32	1908.68
20	10271.32	127.24	292.76	9978.56	3378.56	1781.44
21	9978.56	122.86	297.14	9681.42	3501.42	1658.58
22	9681.42	118.47	301.53	9379.89	3619.89	1540.11
23	9379.89	114.08	305.92	9073.97	3733.97	1426.03
24	9073.97	109.69	310.31	8763.66	3843.66	1316.34
25	8763.66	105.31	314.69	8448.97	3948.97	1211.03
26	8448.97	100.92	319.08	8129.89	4049.89	1110.11
27	8129.89	96.53	323.47	7806.42	4146.42	1013.58
28	7806.42	92.14	327.86	7478.56	4238.56	921.44
29	7478.56	87.76	332.24	7146.32	4326.32	833.68
30	7146.32	83.37	336.63	6809.69	4409.69	750.31
31	6809.69	78.98	341.02	6468.67	4488.67	671.33
32	6468.67	74.59	345.41	6123.26	4563.26	596.74
33	6123.26	70.2	349.8	5773.46	4633.46	526.54
34	5773.46	65.82	354.18	5419.28	4699.28	460.72
35	5419.28	61.43	358.57	5060.71	4760.71	399.29
36	5060.71	57.04	362.96	4697.75	4817.75	342.25
37	4697.75	52.65	367.35	4330.4	4870.4	289.6
38	4330.4	48.27	371.73	3958.67	4918.67	241.33
39	3958.67	43.88	376.12	3582.55	4962.55	197.45
40	3582.55	39.49	380.51	3202.04	5002.04	157.96
41	3202.04	35.1	384.9	2817.14	5037.14	122.86
42	2817.14	30.71	389.29	2427.85	5067.85	92.15
43	2427.85	26.33	393.67	2034.18	5094.18	65.82
44	2034.18	21.94	398.06	1636.12	5116.12	43.88
45	1636.12	17.55	402.45	1233.67	5133.67	26.33
46	1233.67	13.16	406.84	826.83	5146.83	13.17
47	826.83	8.78	411.22	415.61	5155.61	4.39
48	415.61	4.39	415.61	0	5160	0

It is told in the question that to pay off the loan, 14 payments are remaining.

So, the total amount to be paid off =  Principal + Interest = $5,419.28 + $460.72 = $5,880.

Working :-

Payment left	Months	Interest	Principal
1	35	61.43	358.57
2	36	57.04	362.96
3	37	52.65	367.35
4	38	48.27	371.73
5	39	43.88	376.12
6	40	39.49	380.51
7	41	35.1	384.9
8	42	30.71	389.29
9	43	26.33	393.67
10	44	21.94	398.06
11	45	17.55	402.45
12	46	13.16	406.84
13	47	8.78	411.22
14	48	4.39	415.61
		460.72	5419.28