Question

A man is planning to retire in 25 years. He wishes to deposit a regular amount every three
months until he retires, so that, beginning of one year following his retirement, he will
receive annual payments of $60,000 for the next 10 years. How much must he deposit if
the interest rate is 6 percent compounded quarterly?

Answer 1

solution

Present value of benefits at retirement

$Duration\ n=10\ years$

$Payments\ p= 60,000$

$Interest\ r=0.06$

Compounding is done quarterly. Therefore, the effective annual rate is

$$i= (1+\frac{0.06 }{4 })^4-1=0.061364$$

$$A= p * \frac{1-(1+i)^{{-n}} }{i}$$

$$= 60,000 * \frac{1-(1.061364)^{-10} }{0.061364}= 438,766.34272$$

The deposits to be accumulated quarterly (every three months) should equal 438766.34272

$$A = c \ * \frac{(1+\frac{r}{4})^{t*4}-1}{\frac{r}{4} }$$

$$438,766.34272 = c \ * \frac{(1+\frac{0.06}{4})^{25*4}-1}{\frac{0.06}{4} }$$

$$438,766.34273= 228.803*c$$

$$C= 1,917.6596$$

Answer. He must deposit $ 1,917.6596