Question

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

Answer 1

Answer:

Worth of scholarship today =  $1,000,000

Explanation:

The value of the scholarship can be determined using the present value of a growing perpetuity. A growing perpetuity is an indefinite annual payment that increases by a constant percentage.

The applicable formula is given below;

PV = A/r-g

A-annual payment  one year from now - 35,000

r- interest discount rate - 9.,

g- growth rate - 5.5

The value of the gifts today

= 35,000/(0.09-0.055)

= $1,000,000