A scholarship fund has $50,000 in it today and it earns interest at j₂ = 8%.From this amount,you wish to pay out semi-annual scholarships of $R,first scholarship 6-months from now,and each succeeding semi-annual scholarship thereafter increases by $50 forever.What is R?

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Quizplus · Accepted Answer

The first scholarship is $R, the second is $R + $50, the third is $R + $100, and so on. The present value of this infinite geometric series is:PV = R/(1 - (1 + 0.08/2)^(-1)) = R/0.04 = 25RSince the fund has $50,000 in it today, we have:25R = 50,000R = $2,000

A Scholarship Fund Has $50,000 in It Today and It