Whassamatter U.sets up a scholarship fund.The first scholarship is $1000 and is paid today,with each succeeding annual scholarship increasing by $10 a year forever.If the fund earns interest at j₁ = 10%,how much money is needed today?

Question

Quizplus · Accepted Answer

The present value of the scholarship fund is the sum of the present values of each scholarship. The first scholarship is $1000, and each succeeding scholarship increases by $10 a year forever. So, the second scholarship is $1010, the third scholarship is $1020, and so on. The present value of each scholarship is the amount of money that would need to be invested today at 10% interest to earn the amount of the scholarship in the future. The present value of the first scholarship is $1000, the present value of the second scholarship is $1010/1.1 = $918.18, the present value of the third scholarship is $1020/1.1^2 = $843.80, and so on. The sum of the present values of all the scholarships is the present value of the scholarship fund. The sum of the present values of the first 100 scholarships is $1000 + $918.18 + $843.80 + ... + $1100 = $11,000. So, the present value of the scholarship fund is $11,000.