Question

You take a fixed-rate, amortizing, 7-year loan to buy a car. The loan amount is $130,000, the APR is 4.8%. Payment is expected at the end of each month. How much is pure interest in your end-of-month 24 payment assuming all payments were made on time and no prepayments were made?

Answer 1

Sol:

Loan amount (PV) = $130,000

APR = 4.8%, Monthly = 4.8 / 12 = 0.40%

Period (NPER) = 7 years, Monthly = 12 * 7 = 84

To determine pure interest in your end-of-month 24 payment:

Amortization Schedule

PV	-130,000
NPER	84
Rate	0.40%
Monthly payment	$1,825.22
Months	Opening balance	Monthly payment	Principal	Interest	Closing balance
1	130,000	$1,825.22	$1,305.22	520	$128,694.78
2	$128,694.78	$1,825.22	$1,310.44	514.7791	$127,384.35
3	$127,384.35	$1,825.22	$1,315.68	509.5374	$126,068.67
4	$126,068.67	$1,825.22	$1,320.94	504.2747	$124,747.73
5	$124,747.73	$1,825.22	$1,326.23	498.9909	$123,421.50
6	$123,421.50	$1,825.22	$1,331.53	493.686	$122,089.97
7	$122,089.97	$1,825.22	$1,336.86	488.3599	$120,753.12
8	$120,753.12	$1,825.22	$1,342.20	483.0125	$119,410.91
9	$119,410.91	$1,825.22	$1,347.57	477.6436	$118,063.34
10	$118,063.34	$1,825.22	$1,352.96	472.2534	$116,710.38
11	$116,710.38	$1,825.22	$1,358.37	466.8415	$115,352.00
12	$115,352.00	$1,825.22	$1,363.81	461.408	$113,988.19
13	$113,988.19	$1,825.22	$1,369.26	455.9528	$112,618.93
14	$112,618.93	$1,825.22	$1,374.74	450.4757	$111,244.19
15	$111,244.19	$1,825.22	$1,380.24	444.9768	$109,863.95
16	$109,863.95	$1,825.22	$1,385.76	439.4558	$108,478.19
17	$108,478.19	$1,825.22	$1,391.30	433.9128	$107,086.89
18	$107,086.89	$1,825.22	$1,396.87	428.3476	$105,690.02
19	$105,690.02	$1,825.22	$1,402.46	422.7601	$104,287.56
20	$104,287.56	$1,825.22	$1,408.07	417.1503	$102,879.50
21	$102,879.50	$1,825.22	$1,413.70	411.518	$101,465.80
22	$101,465.80	$1,825.22	$1,419.35	405.8632	$100,046.45
23	$100,046.45	$1,825.22	$1,425.03	400.1858	$98,621.42
24	$98,621.42	$1,825.22	$1,430.73	394.4857	$97,190.69
25	$97,190.69	$1,825.22	$1,436.45	388.7627	$95,754.23
26	$95,754.23	$1,825.22	$1,442.20	383.0169	$94,312.03
27	$94,312.03	$1,825.22	$1,447.97	377.2481	$92,864.07
28	$92,864.07	$1,825.22	$1,453.76	371.4563	$91,410.31
29	$91,410.31	$1,825.22	$1,459.57	365.6412	$89,950.73
30	$89,950.73	$1,825.22	$1,465.41	359.8029	$88,485.32
31	$88,485.32	$1,825.22	$1,471.27	353.9413	$87,014.04
32	$87,014.04	$1,825.22	$1,477.16	348.0562	$85,536.88
33	$85,536.88	$1,825.22	$1,483.07	342.1475	$84,053.82
34	$84,053.82	$1,825.22	$1,489.00	336.2153	$82,564.82
35	$82,564.82	$1,825.22	$1,494.96	330.2593	$81,069.86
36	$81,069.86	$1,825.22	$1,500.94	324.2794	$79,568.92
37	$79,568.92	$1,825.22	$1,506.94	318.2757	$78,061.98
38	$78,061.98	$1,825.22	$1,512.97	312.2479	$76,549.01
39	$76,549.01	$1,825.22	$1,519.02	306.1961	$75,029.99
40	$75,029.99	$1,825.22	$1,525.10	300.12	$73,504.90
41	$73,504.90	$1,825.22	$1,531.20	294.0196	$71,973.70
42	$71,973.70	$1,825.22	$1,537.32	287.8948	$70,436.38
43	$70,436.38	$1,825.22	$1,543.47	281.7455	$68,892.91
44	$68,892.91	$1,825.22	$1,549.64	275.5716	$67,343.26
45	$67,343.26	$1,825.22	$1,555.84	269.3731	$65,787.42
46	$65,787.42	$1,825.22	$1,562.07	263.1497	$64,225.36
47	$64,225.36	$1,825.22	$1,568.31	256.9014	$62,657.04
48	$62,657.04	$1,825.22	$1,574.59	250.6282	$61,082.45
49	$61,082.45	$1,825.22	$1,580.89	244.3298	$59,501.57
50	$59,501.57	$1,825.22	$1,587.21	238.0063	$57,914.36
51	$57,914.36	$1,825.22	$1,593.56	231.6574	$56,320.80
52	$56,320.80	$1,825.22	$1,599.93	225.2832	$54,720.87
53	$54,720.87	$1,825.22	$1,606.33	218.8835	$53,114.53
54	$53,114.53	$1,825.22	$1,612.76	212.4581	$51,501.78
55	$51,501.78	$1,825.22	$1,619.21	206.0071	$49,882.57
56	$49,882.57	$1,825.22	$1,625.69	199.5303	$48,256.88
57	$48,256.88	$1,825.22	$1,632.19	193.0275	$46,624.69
58	$46,624.69	$1,825.22	$1,638.72	186.4988	$44,985.97
59	$44,985.97	$1,825.22	$1,645.27	179.9439	$43,340.70
60	$43,340.70	$1,825.22	$1,651.85	173.3628	$41,688.85
61	$41,688.85	$1,825.22	$1,658.46	166.7554	$40,030.39
62	$40,030.39	$1,825.22	$1,665.09	160.1216	$38,365.29
63	$38,365.29	$1,825.22	$1,671.75	153.4612	$36,693.54
64	$36,693.54	$1,825.22	$1,678.44	146.7742	$35,015.10
65	$35,015.10	$1,825.22	$1,685.16	140.0604	$33,329.94
66	$33,329.94	$1,825.22	$1,691.90	133.3198	$31,638.05
67	$31,638.05	$1,825.22	$1,698.66	126.5522	$29,939.38
68	$29,939.38	$1,825.22	$1,705.46	119.7575	$28,233.92
69	$28,233.92	$1,825.22	$1,712.28	112.9357	$26,521.64
70	$26,521.64	$1,825.22	$1,719.13	106.0866	$24,802.51
71	$24,802.51	$1,825.22	$1,726.01	99.21005	$23,076.51
72	$23,076.51	$1,825.22	$1,732.91	92.30603	$21,343.60
73	$21,343.60	$1,825.22	$1,739.84	85.37439	$19,603.76
74	$19,603.76	$1,825.22	$1,746.80	78.41502	$17,856.95
75	$17,856.95	$1,825.22	$1,753.79	71.42782	$16,103.17
76	$16,103.17	$1,825.22	$1,760.80	64.41267	$14,342.36
77	$14,342.36	$1,825.22	$1,767.85	57.36945	$12,574.52
78	$12,574.52	$1,825.22	$1,774.92	50.29807	$10,799.60
79	$10,799.60	$1,825.22	$1,782.02	43.1984	$9,017.58
80	$9,017.58	$1,825.22	$1,789.15	36.07032	$7,228.44
81	$7,228.44	$1,825.22	$1,796.30	28.91374	$5,432.13
82	$5,432.13	$1,825.22	$1,803.49	21.72853	$3,628.65
83	$3,628.65	$1,825.22	$1,810.70	14.51458	$1,817.94
84	$1,817.94	$1,825.22	$1,817.94	7.271
$10,995.87

Therefore your total pure interest payments till 24 months will be $10,995.87 and your end of 24th month payment will be $394.49.

Working