Question

27. Gotham billionaire Bruce Wayne has purchased a house for 102,000,000. Wayne makes a down payment of 2,000,000 and finances the rest of the mortgage through 15 years of end of month payments. The first payment is due exactly one month from today. The nominal rate of interest is 15% convertible monthly. The first 120 payments all contain 100,000 in principal. The last 60 payments go as follows. The 121st payment is X. Then each subsequent payment is 10% greater than the preceding one. a. Determine X. b. Determine the interest paid in the last five years of the loan. c. Determine the interest paid in the 13th year of the loan.

Answer 1

Finance amount = 102,000,000 – 2,000,000 = 100,000,000

This is finances through 15 years loan and so nper = 15*12 = 180. Rate = 15%/12

Let us now make a loan amortization table as shown below:

(a): X = 28,996.8118. This will be rounded to 28,997

(b): Interest paid in the last 5 years (or last 60 months) = 55,217,476.09. This will be rounded to 55,217,476

(c): Interest paid in 13th year means interest paid from month 144 to 155. Interest amount = 12,549,452

The table is shown below:

Period	Loan balance at the start of the month	Principal repayment	Interest	Total payment	Loan balance at the start of the month
1	100,000,000	100,000	1,250,000	1,350,000	99,900,000
2	99,900,000	100,000	1,248,750	1,348,750	99,800,000
119	88,200,000	100,000	1,102,500	1,202,500	88,100,000
120	88,100,000	100,000	1,101,250	1,201,250	88,000,000
121	88,000,000	28,997	1,100,000	1,128,997	87,971,003
122	87,971,003	31,896	1,099,638	1,131,534	87,939,107
167	65,040,460	2,324,951	813,006	3,137,957	62,715,509
168	62,715,509	2,557,446	783,944	3,341,390	60,158,063
169	60,158,063	2,813,190	751,976	3,565,166	57,344,873
170	57,344,873	3,094,510	716,811	3,811,320	54,250,363
171	54,250,363	3,403,960	678,130	4,082,090	50,846,403
172	50,846,403	3,744,357	635,580	4,379,937	47,102,046
173	47,102,046	4,118,792	588,776	4,707,568	42,983,254
174	42,983,254	4,530,671	537,291	5,067,962	38,452,583
175	38,452,583	4,983,739	480,657	5,464,396	33,468,844
176	33,468,844	5,482,112	418,361	5,900,473	27,986,732
177	27,986,732	6,030,324	349,834	6,380,158	21,956,408
178	21,956,408	6,633,356	274,455	6,907,811	15,323,052
179	15,323,052	7,296,692	191,538	7,488,230	8,026,361
180	8,026,361	8,026,361	100,330	8,126,690	0