A wealthy benefactor just donated some money to the local college.This gift was established to provide scholarships for worthy students.The first scholarships will be granted one year from now for a total of $35,000.Annually thereafter,the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation.The scholarship fund will last indefinitely.What is the value of this gift today at a discount rate of 9 percent?

Question

Quizplus · Accepted Answer

This is a problem involving the concept of perpetuity. The formula to calculate the present value of a perpetuity is PV = PMT / r, where PV is the present value, PMT is the annual payment, and r is the discount rate. However, since the payments grow at a constant rate (g), we use a modified formula: PV = PMT / (r - g), where g is the growth rate. Here, PMT = $35,000, r = 9% or 0.09, and g = 5.5% or 0.055. Plugging these values into the modified formula gives us PV = $35,000 / (0.09 - 0.055) = $35,000 / 0.035 = $1,000,000.

A Wealthy Benefactor Just Donated Some Money to the Local