Ashley borrows $3,000 for 10 years at 13% annual effective. She pays the interes

Question

Ashley borrows $3,000 for 10 years at 13% annual effective. She pays the interest yearly, and the principal by means of two sinking funds. One-third of the principal is repaid by a sinking fund earning 17% effective annually, and the other two-thirds by a sinking fund earning 12% effective annually.
(a) Find Ashley's total annual payment and the rate of interest she is really paying on her loan.
(b) Redo (a) if Ashley puts one-third of her total sinking fund deposit in the 17% fund and two-thirds into the 12% fund.

Explanation / Answer

One-third of the principal is repaid by earning 17% = PMT(17%,10,,-3000/3) = 44.66

Two-third of the principal is repaid by earning 12% = PMT(12%,10,,-3000*2/3) = 113.97

Annual interest payments = 3000*13% = 390

a)

Annual payments = 390 + 113.97 + 44.66 = 548.62

Interest rate = RATE(10,548.62 ,-3000) = 12.81%

b)

Annual Sinking fund deposits = X

X/3 into 17%, 2X/3 into 12%

X/3*FV(17%,10,-1) + 2X/3*FV(12%,10,-1) = 3000

X/3 * 22.39 + 2X/3*17.55 = 3000

19.16*X = 3000

X = 156.55

Annual payments = 390 + 156.55= 546.55

Interest rate = RATE(10,546.55,-3000) = 12.71%

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