Question

You are head of the schwartz family endowment for the arts. you have decided to fund an arts school in the san francisco bay area in perpetuity. every 5 ​years, you will give the school $ 1 comma 000 comma 000. the first payment will occur 5 years from today. if the interest rate is 5.9 % per​ year, what is the present value of your​ gift?

Answer 1

Answer: $3,012,727.95

Step-by-step explanation:

Given the following :

Payment per period = 1,000,000

First payment will occur five years from today

Interest rate = 5.9% per annum

Firstly:

Calculating the interest rate over the 5 year period :

Interest rate = [ (1 + actual interest rate)^n - 1)

Interest rate = [ ( 1 + 0.059)^5 - 1)

Interest rate = [ 1.059^5 - 1]

Interest rate = 1.331925091729299 - 1

Interest rate = 0.331925091729299

Therefore, present value of gift equals :

Payment per period ÷ interest rate

1,000,000 ÷ 0.331925091729299

PV of gift = $3,012,727.94650772