Question

A 45-year old man puts $1000 in a retirement account at the end of each quarter until he reaches the age of 60 and makes no further deposits. If the account pays 8% interest compounded quarterly, how much will be in the account when he retires at 65?

Answer 1

The account will have $292,526.3494 by the time he retired

Explanation:

The expression for the total amount earned from the investment is;

A=P(1+r/n)^nt

where;

A=future value of investment

P=present value of investment

r=annual interest rate

n=number of periods

t=number of years

In our case;

P=deposits $1000 every 3 months for 15 years

A year has 4 periods

The present value, P=1000×4×15=$60,000

r=8%=8/100=0.08

n=4

t=(65-45)=20 years

replacing;

A=60,000(1+0.08/4)^(4×20)

A=60,000(1.02)^80

A=292,526.3494

The account will have $292,526.3494 by the time he retired