In 30years, Adam plans to set up a scholarship fund for his university that pays out $100,000/year in perpetuity with an annually compounded discount rate of 5%. In order to set up the fund in 30 years, how much does Adam need to save each year( starting this year) assuming he gets a semi- annually compounded return of 10% on his savings for the next years?

Answer:

Formula for calculation of Present value of perpetuity

Value of a perpetuity = C/ r

Where,

Value of a perpetuity is the sum of the present values of its expected future cash flows at the time (t=0) =?

Annual payments C = $100,000

Interest rate r = 5% per year

Therefore,

Value of a perpetuity = $100,000/5%

= $100,000/0.05

= $2,000,000

Now we know that Adam required $2,000,000 amount for perpetuity and we have to calculate annual savings to meet this requirement

We can use FV of an Annuity formula to calculate the annual deposits

FV = PMT *{(1+i) ^n−1} / i

Where,

Future value of deposits after retirement FV = $2,000,000

PMT = Annual deposits =?

n = N = number of payments = 30 (years)

i = I/Y = interest rate per year = 10%, but compounded semiannually; therefore effective annual interest rate is (1+10%/2) ^2 = 10.25% per year

Therefore,

$2,000,000 = annual deposits *{(1+10.25%) ^30−1} /10.25%

Annual deposits = $11,595.56

Therefore Adam needs to deposit $11,595.56 each year for 30 years