Question

Payments on a $10000 loan are made quarterly in arrears (that is, at the end of each quarter) for 10 years. The annual effective rate of interest is 7%. Find the principal outstanding after the 6th payment, and the amount of principal in the 14th payment (using the amortization method in both cases).

Answer 1

Solution:

Loan amount = $10,000

Interest rate = 7% per year, 1.75% quarterly rate

Payment terms = 40 equal quarterly payments

Quarterly loan payment = Loan amount / Cumulative PV Factor at 1.75% for 40 periods

= $10,000 / 28.59423 = $349.72

Loan Amortization schedule
Period	Opening balance	Interest (Opening balance* 1.75%)	EMI Payment	Closing Balance (Opening + Interest - EMI)
1	$10,000.00	$175.00	$349.72	$9,825.28
2	$9,825.28	$171.94	$349.72	$9,647.50
3	$9,647.50	$168.83	$349.72	$9,466.61
4	$9,466.61	$165.67	$349.72	$9,282.56
5	$9,282.56	$162.44	$349.72	$9,095.28
6	$9,095.28	$159.17	$349.72	$8,904.73
7	$8,904.73	$155.83	$349.72	$8,710.84
8	$8,710.84	$152.44	$349.72	$8,513.56
9	$8,513.56	$148.99	$349.72	$8,312.83
10	$8,312.83	$145.47	$349.72	$8,108.59
11	$8,108.59	$141.90	$349.72	$7,900.77
12	$7,900.77	$138.26	$349.72	$7,689.31
13	$7,689.31	$134.56	$349.72	$7,474.15
14	$7,474.15	$130.80	$349.72	$7,255.23
15	$7,255.23	$126.97	$349.72	$7,032.48
16	$7,032.48	$123.07	$349.72	$6,805.83
17	$6,805.83	$119.10	$349.72	$6,575.21
18	$6,575.21	$115.07	$349.72	$6,340.55
19	$6,340.55	$110.96	$349.72	$6,101.79
20	$6,101.79	$106.78	$349.72	$5,858.85
21	$5,858.85	$102.53	$349.72	$5,611.66
22	$5,611.66	$98.20	$349.72	$5,360.15
23	$5,360.15	$93.80	$349.72	$5,104.23
24	$5,104.23	$89.32	$349.72	$4,843.84
25	$4,843.84	$84.77	$349.72	$4,578.88
26	$4,578.88	$80.13	$349.72	$4,309.29
27	$4,309.29	$75.41	$349.72	$4,034.99
28	$4,034.99	$70.61	$349.72	$3,755.88
29	$3,755.88	$65.73	$349.72	$3,471.89
30	$3,471.89	$60.76	$349.72	$3,182.92
31	$3,182.92	$55.70	$349.72	$2,888.90
32	$2,888.90	$50.56	$349.72	$2,589.74
33	$2,589.74	$45.32	$349.72	$2,285.34
34	$2,285.34	$39.99	$349.72	$1,975.61
35	$1,975.61	$34.57	$349.72	$1,660.47
36	$1,660.47	$29.06	$349.72	$1,339.81
37	$1,339.81	$23.45	$349.72	$1,013.53
38	$1,013.53	$17.74	$349.72	$681.55
39	$681.55	$11.93	$349.72	$343.76
40	$343.76	$5.96	$349.72	$0.00

Refer above table:

Principal outstanding after 6th payment = $8,904.73

Amount of principal in 14th payment = $349.72 - $130.80 = $218.92