Question

A donor established a AU scholarship that will pay $13000 per year to a student. The scholarship will be awarded for the first time in September of 2025 (i.e., the first payment occurs three years from now). The donor decides that the scholarship should be provided in perpetuity. The AU foundation manages investments like this for the Business School. The Foundation anticipates earning an APR of 7.5% per year on the invested funds. What is the amount of the donation that must be given to the AU Foundation today to endow this scholarship.

Answer 1

Initially, we need to calculate the present value of perpetuity in september 2025 (three Years from now). Then we need to discount that value back by three years, to find out the amount of donation needed today.

Value of the Perpetuity can be calculated as: P/r; where P is the value of the payment every period and r is the interest rate per period.

So, Value of Perpetuity in september 2025= 13000/7.5%= $173333.33.

Discounting back to three years at 7.5%, we get,

X/(1+r)^n= 173333.33/(1+7.5%)^3= $139526.50

So, the amount of donation that should be given as scholarship today is $139526.50