Question

A 60 year old alum donates 300000 today (at t=0) to the College for an annual scholarship that will start with the first scholarship payment in t=20, and thereafter, the scholarship amount will grow at a rate of 3% / year to account for inflation. If the College's discount rate is 7%, how large will the first payment in t=20 be?

Answer 1

GIVEN: Present Value at t-0 = 300000

Discount Rate (r) = 7%

Now, we need first payment in t=20

Therefore, as per discounting technique, we have

Present Value = Future Value/(1+r)^t

300000 = Payment after 20th year/(1+.07)²⁰

  300000 = Payment after 20th year X PVF(7%, 20 years)

300000 = Payment after 20th year X 0.2584

Payment after 20th year = 300000/0.2584

  Payment after 20th year = 1160990.71

Therefore, the first payment in t=20 is 1160990.71

Note: Since, the question has asked only for the first payment,therefore, the growth of scholarship amount @ 3% p.a. from 21st year onwards is not taken into consideration.