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Construct a loan amortization schedule for a 30-year, 8.65% loan of $15,000,000. The loan requires equal,...

Construct a loan amortization schedule for a 30-year, 8.65% loan of $15,000,000. 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?

Expert Solution

Given

Amount Financed	15000000
Installment	Yearly
Interest	8.65%
Compounding	Monthly
Effective Annual Interest rate	9.0%
Total No. of payment	30
Yearly Installment	1460215.095

We have Calculated Effective Interest rate because the interest is compounded monthly

Formula for effective interest rate is

=

= 0.09 or 9%

Formula for Annual Installment

So the Annual Installments would be

= = 1460215.09

Amortization Schedule

Payment	Instalment	Interest	Principal	Cumulative Interest	Cumulative Principal	Principal Balance
						15000000
1	1460215.09	1350196.75	110018.35	1350196.75	110018.35	14889981.65
2	1460215.09	1340293.65	119921.44	2690490.40	229939.79	14770060.21
3	1460215.09	1329499.15	130715.94	4019989.55	360655.73	14639344.27
4	1460215.09	1317733.00	142482.09	5337722.56	503137.82	14496862.18
5	1460215.09	1304907.74	155307.35	6642630.30	658445.17	14341554.83
6	1460215.09	1290928.05	169287.05	7933558.35	827732.22	14172267.78
7	1460215.09	1275689.99	184525.10	9209248.34	1012257.33	13987742.67
8	1460215.09	1259080.31	201134.78	10468328.65	1213392.11	13786607.89
9	1460215.09	1240975.54	219239.55	11709304.19	1432631.66	13567368.34
10	1460215.09	1221241.11	238973.99	12930545.30	1671605.65	13328394.35
11	1460215.09	1199730.31	260484.78	14130275.62	1932090.43	13067909.57
12	1460215.09	1176283.27	283931.83	15306558.88	2216022.25	12783977.75
13	1460215.09	1150725.68	309489.42	16457284.56	2525511.67	12474488.33
14	1460215.09	1122867.57	337347.52	17580152.13	2862859.19	12137140.81
15	1460215.09	1092501.87	367713.22	18672654.01	3230572.42	11769427.58
16	1460215.09	1059402.86	400812.24	19732056.86	3631384.66	11368615.34
17	1460215.09	1023324.50	436890.60	20755381.36	4068275.25	10931724.75
18	1460215.09	983998.61	476216.48	21739379.97	4544491.73	10455508.27
19	1460215.09	941132.88	519082.21	22680512.86	5063573.94	9936426.06
20	1460215.09	894408.68	565806.42	23574921.53	5629380.36	9370619.64
21	1460215.09	843478.68	616736.42	24418400.21	6246116.78	8753883.22
22	1460215.09	787964.31	672250.78	25206364.52	6918367.56	8081632.44
23	1460215.09	727452.92	732762.17	25933817.45	7651129.74	7348870.26
24	1460215.09	661494.72	798720.38	26595312.16	8449850.12	6550149.88
25	1460215.09	589599.41	870615.69	27184911.57	9320465.81	5679534.19
26	1460215.09	511232.57	948982.52	27696144.14	10269448.33	4730551.67
27	1460215.09	425811.70	1034403.40	28121955.84	11303851.72	3696148.28
28	1460215.09	332701.83	1127513.27	28454657.66	12431364.99	2568635.01
29	1460215.09	231210.84	1229004.25	28685868.51	13660369.24	1339630.76
30	1460215.09	120584.34	1339630.76	28806452.85	15000000.00	0.00

Total Interest Paid is 28806452.85, Which is nothing but the last value of accumulated interest.

Formulas Used

Interest for t =

Principal Paid = Annual Installment - Interest

Principal Balance for t =

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