Question

A- 1. Construct a loan amortization schedule for a 15-year, 7.75% loan of $10,000,000. The loan requires equal, end-of-year payments, and interest is compounded monthly.

- What is the total amount of interest paid over the life of the loan?

2. Re-construct this amortization schedule assuming that interest is compounded annually.

- What total amount of interest is paid over the life of the loan? - What is the difference between those total interest amounts?

3. Assume that in sections 1 and 2 above, there is a balloon payment requirement after 10 years

. - What is the balloon payment in section 1? - What is the balloon payment in Section 2? - What is the difference between these amounts?

Answer 1

Loan amortization schedule - monthly compounding
Loan	10000000
Interest rate	7.75%
Tenure	15	year
Repayment every month	$94,127.58
Total interest paid back	$6,942,963.55
Month	Loan value beginning	Interest	Principal	Repayment	Loan value at end
1	10000000.00	64583.33	$29,544.24	$94,127.58	$9,970,455.76
2	9970455.76	64392.53	$29,735.05	$94,127.58	$9,940,720.71
3	9940720.71	64200.49	$29,927.09	$94,127.58	$9,910,793.62
4	9910793.62	64007.21	$30,120.37	$94,127.58	$9,880,673.26
5	9880673.26	63812.68	$30,314.89	$94,127.58	$9,850,358.36
6	9850358.36	63616.9	$30,510.68	$94,127.58	$9,819,847.68
7	9819847.68	63419.85	$30,707.73	$94,127.58	$9,789,139.96
8	9789139.96	63221.53	$30,906.05	$94,127.58	$9,758,233.91
9	9758233.91	63021.93	$31,105.65	$94,127.58	$9,727,128.26
10	9727128.26	62821.04	$31,306.54	$94,127.58	$9,695,821.73
11	9695821.73	62618.85	$31,508.73	$94,127.58	$9,664,313.00
12	9664313.00	62415.35	$31,712.22	$94,127.58	$9,632,600.78
13	9632600.78	62210.55	$31,917.03	$94,127.58	$9,600,683.75
14	9600683.75	62004.42	$32,123.16	$94,127.58	$9,568,560.59
15	9568560.59	61796.95	$32,330.62	$94,127.58	$9,536,229.97
16	9536229.97	61588.15	$32,539.42	$94,127.58	$9,503,690.55
17	9503690.55	61378	$32,749.57	$94,127.58	$9,470,940.97
18	9470940.97	61166.49	$32,961.08	$94,127.58	$9,437,979.89
19	9437979.89	60953.62	$33,173.96	$94,127.58	$9,404,805.93
20	9404805.93	60739.37	$33,388.20	$94,127.58	$9,371,417.73
21	9371417.73	60523.74	$33,603.84	$94,127.58	$9,337,813.90
22	9337813.90	60306.71	$33,820.86	$94,127.58	$9,303,993.03
23	9303993.03	60088.29	$34,039.29	$94,127.58	$9,269,953.75
24	9269953.75	59868.45	$34,259.12	$94,127.58	$9,235,694.62
25	9235694.62	59647.19	$34,480.38	$94,127.58	$9,201,214.24
26	9201214.24	59424.51	$34,703.07	$94,127.58	$9,166,511.18
27	9166511.18	59200.38	$34,927.19	$94,127.58	$9,131,583.99
28	9131583.99	58974.81	$35,152.76	$94,127.58	$9,096,431.22
29	9096431.22	58747.78	$35,379.79	$94,127.58	$9,061,051.43
30	9061051.43	58519.29	$35,608.28	$94,127.58	$9,025,443.15
31	9025443.15	58289.32	$35,838.25	$94,127.58	$8,989,604.89
32	8989604.89	58057.86	$36,069.71	$94,127.58	$8,953,535.18
33	8953535.18	57824.91	$36,302.66	$94,127.58	$8,917,232.52
34	8917232.52	57590.46	$36,537.12	$94,127.58	$8,880,695.41
35	8880695.41	57354.49	$36,773.08	$94,127.58	$8,843,922.32
36	8843922.32	57117	$37,010.58	$94,127.58	$8,806,911.75
37	8806911.75	56877.97	$37,249.60	$94,127.58	$8,769,662.14
38	8769662.14	56637.4	$37,490.17	$94,127.58	$8,732,171.97
39	8732171.97	56395.28	$37,732.30	$94,127.58	$8,694,439.67
40	8694439.67	56151.59	$37,975.99	$94,127.58	$8,656,463.68
41	8656463.68	55906.33	$38,221.25	$94,127.58	$8,618,242.44
42	8618242.44	55659.48	$38,468.09	$94,127.58	$8,579,774.34
43	8579774.34	55411.04	$38,716.53	$94,127.58	$8,541,057.81
44	8541057.81	55161	$38,966.58	$94,127.58	$8,502,091.24
45	8502091.24	54909.34	$39,218.24	$94,127.58	$8,462,873.00
46	8462873.00	54656.05	$39,471.52	$94,127.58	$8,423,401.48
47	8423401.48	54401.13	$39,726.44	$94,127.58	$8,383,675.04
48	8383675.04	54144.57	$39,983.01	$94,127.58	$8,343,692.03
49	8343692.03	53886.34	$40,241.23	$94,127.58	$8,303,450.80

Same is continued till 180 months

Loan amortization schedule - yearly compounding
Loan	10000000
Interest rate	7.75%
Tenure	15	year
Repayment every year	$1,150,522.46
Total interest paid back	$7,257,836.93
Year	Loan value beginning	Interest	Principal	Repayment	Loan value at end
1	10000000.00	775000.00	$375,522.46	$1,150,522.46	$9,624,477.54
2	9624477.54	745897.01	$404,625.45	$1,150,522.46	$9,219,852.09
3	9219852.09	714538.54	$435,983.93	$1,150,522.46	$8,783,868.16
4	8783868.16	680749.78	$469,772.68	$1,150,522.46	$8,314,095.48
5	8314095.48	644342.40	$506,180.06	$1,150,522.46	$7,807,915.42
6	7807915.42	605113.44	$545,409.02	$1,150,522.46	$7,262,506.40
7	7262506.40	562844.25	$587,678.22	$1,150,522.46	$6,674,828.19
8	6674828.19	517299.18	$633,223.28	$1,150,522.46	$6,041,604.91
9	6041604.91	468224.38	$682,298.08	$1,150,522.46	$5,359,306.83
10	5359306.83	415346.28	$735,176.18	$1,150,522.46	$4,624,130.64
11	4624130.64	358370.12	$792,152.34	$1,150,522.46	$3,831,978.31
12	3831978.31	296978.32	$853,544.14	$1,150,522.46	$2,978,434.16
13	2978434.16	230828.65	$919,693.81	$1,150,522.46	$2,058,740.35
14	2058740.35	159552.38	$990,970.08	$1,150,522.46	$1,067,770.27
15	1067770.27	82752.20	$1,067,770.27	$1,150,522.46	($0.00)

Difference in interest amounts: 314,873.37

The balloon repayment would be the sum of principal repayment till that time of 10 years or 120 months

For monthly compounding that value is: 5330,269.22

For annual compounding that value is: 5375,869.36

Difference is: 45,600.14