Question

Deposits to create a perpetuity You have decided to endow your favorite university

with a scholarship. It is expected to cost $6,000 per year to attend the university

into perpetuity. You expect to give the university the endowment in 10 years and

will accumulate it by making equal annual (end-of-year) deposits into an account.

The rate of interest is expected to be 10% 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 10 years to accumu-

late the required amount?

Answer 1

a. $\frac{60}{0.1}=60 000$

b.$FV=A\times\frac{(1+r)^n-1}{r}$

FV= 60 000

$60 000=A\times\frac{(1+0.1)^{10}-1}{0.1}$

$60 000=A\times15.94$

A=3764.72