Answer to Question #215739 in Financial Math for Burak

Question

You have decided to endow Faculty of Business, Dokuz Eylul University with a scholarship. It is expected to cost ​$3,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 9 years and will accumulate it by making equal annual​ (end-of-year) deposits into an account. The rate of interest is expected to be 8​% for all future time periods.

a. How large must the endowment​ be?

b. How much must you deposit at the end of each of the next 9 years to accumulate the required​ amount?

Answer 1

Let S be the required amount. Annual income from the deposit on account after the required amount will be accumulated will be 0.08S. It must cover annual expenses of $3,000.

0.08S = $3,000

S = $3,000 / 0.08 = $37,500

Let x be annual sum, we must to deposit in order to accumulate S.

Then the total sum accumulated in 9 years will be

$S= x+xq+xq^2+\dots+xq^8=x\frac{q^9-1}{q-1}$

where q=1+r=1.08, and r=0.08 is the interest rate.

$x=S\frac{q-1}{q^9-1}=37500\cdot\frac{0.08}{1.08^9-1}=3003$

Answer. (a) $3,003; (b) $37,500.