The New York City public school system was awarded a grant o

The New York City public school system was awarded a grant of $50 million over 5 years from the Annenberg Foundation. The foundation deposits its initial donation into an account with an annual interest rate of 6.8% and interest is compounded annually. If the grant dispersed an equal payment at the end of each year, how much should the foundation deposit at the time the grant is announced in order to meet its pledged obligation?

(Please show your work clearly)

Solution

The future value of grant is $50mil. All we have to do is find the PV. Since, yearly equal payments are made, this problem is equivalent to PV of a 5 year annuity.

Deposit Amt = C (1 -(1+ r)^-n)/r where n = no of periods, r = interest rate and C = cash flow/period

                  = 10mil*4.122 = $41.22 million