Question

Prestigious University is offering a new admission and tuition payment plan for all alumni. On the birth of a​ child, parents can guarantee admission to Prestigious if they pay the first​ year's tuition. The university will pay an annual rate of return of 7​% on the deposited​ tuition, and a full refund will be available if the child chooses another university. The tuition is expected to be ​$20,000 a year at Prestigious 18 years from now. What would parents pay today if they just gave birth to a new baby and the child will attend college in 18 ​years? How much is the required payment to secure admission for their child if the interest rate falls to 4​%?

Answer 1

(1): $20,000 is the future value of amount deposited today (i.e. at t = 0) after 18 years and at r = 7%

Let the amount deposited today be "x"

So 20,000 = x*(1.07)^18

or 20,000 = x*3.37993

or x = 20,000/3.37993

= $5,917.28

(2): If rate of interest falls to 4% then 20,000 = x*(1.04)^18

or. 20,000 = x*2.0258

or x = 20,000/2.0258

= $9,872.56