Ralph buys a perpetuity-due paying 500 annually. He deposits the payments into a

Question

Ralph buys a perpetuity-due paying 500 annually. He deposits the payments into a savings account earning interest at an effective annual rate of 10%. Ten years later, before receiving the eleventh payment, Ralph sells the remaining payments of the perpetuity based on an annual effective interest rate of 10%. Using the proceeds from the sale plus the money in the savings account, Ralph purchases an annuity-due paying X per year for 20 years at an effective annual interest rate of 10%. Calculate x. (a) 1145 (b) 1260 (c) 1385 (d) 1525 (e) 1675

Explanation / Answer

amount accumulated in savings account nper 10 rate 10% PMT 500 Fv $7,968.71 sale proceeds = 500/0.1 5000 annuity paid nper 20 rate 10% PV (5000+7968.71) $12,968.71 PMT $1,523.30 so option d is correct

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