Question

B borrows $15,000 for eight years and agrees to make semiannual payments of $1400. The lender receives 10% convertible semiannually on the investment each year for the first six years and 8% convertible semiannually for the last two years. The balance of each payment is invested in a sinking fund earning 6% convertible semiannually. Find the amount by which the sinking fund is short of repaying the loan at the end of the eight years. (Answer: $1,270.48.)

Answer 1

There are 20 payment periods, between periods 1 and 12 the interest of the loan is 750, and between periods 13 and 16 the interest payment is 600. So the principle for the sinking fund from periods 1 to 12 is 650, and from periods 13 to 16 is 800. So I found the future value of the sinking fund in Table 1 Below, which equals 13729.52, and since the loan value remains the same, I take the future value of the sinking fund and subtract it from 15000 (the loan amount) to arrive at the value the sinking fund is short, which is 1270.48.

Table 1

	D	E	F
Loan repayment	Years	Interest(15000*i/100)	Principal	Sinking fund value calculation	Sinking fund value
1400	1	750	650	=F2*1.03^(16-D2)	1012.679
1400	2	750	650	=F3*1.03^(16-D3)	983.1833
1400	3	750	650	=F4*1.03^(16-D4)	954.5469
1400	4	750	650	=F5*1.03^(16-D5)	926.7446
1400	5	750	650	=F6*1.03^(16-D6)	899.752
1400	6	750	650	=F7*1.03^(16-D7)	873.5456
1400	7	750	650	=F8*1.03^(16-D8)	848.1026
1400	8	750	650	=F9*1.03^(16-D9)	823.4006
1400	9	750	650	=F10*1.03^(16-D10)	799.418
1400	10	750	650	=F11*1.03^(16-D11)	776.134
1400	11	750	650	=F12*1.03^(16-D12)	753.5281
1400	12	750	650	=F13*1.03^(16-D13)	731.5807
1400	13	600	800	=F14*1.03^(16-D14)	874.1816
1400	14	600	800	=F15*1.03^(16-D15)	848.72
1400	15	600	800	=F16*1.03^(16-D16)	824
1400	16	600	800	=F17*1.03^(16-D17)	800
					13729.52
				Principal	15000
				Shortage	1270.483

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