) Snoopy borrows 6500 dollars to pay for his new super-deluxe doghouse. To pay o
ID: 2790687 • Letter: #
Question
) Snoopy borrows 6500 dollars to pay for his new super-deluxe doghouse. To pay off the loan, he agrees to make monthly interest payments on the loan, and will also build up a sinking fund with equal monthly deposits to repay the principal with a single payment 22 months from now. If the interest rate on the loan is 7.9 percent, and the interest paid on the sinking fund is 6.3 percent, both nominal convertible monthly, what is Snoopy's total outlay? (Assume the first interest payment and the first sinking fund deposit will both come in one month.) Answer = dollars.
Explanation / Answer
Monthly interest payment on loan = ($6500 * 7.9%)/12 = $42.79 Using future value of annuity formula we can find out the monthly deposit to sinking fund. FV of annuity = P*{[(1+r)^n - 1]/r} FV of annuity = value of sinking fund after 22 months = $6500 P = Monthly deposit = ? r = rate of interest per month = 6.3%/12 = 0.00525 n = no.of months = 22 6500 = P*{[(1+0.00525)^22 - 1]/0.00525} 6500 = P*23.256275 P = 279.49 Monthly deposit to sinking fund = $279.49 Snoopy's total outlay per month = Monthly Interest + Monthly deposit to sinking fund = $42.79 + $279.49 = $322.28
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