At age
18,
someone sets up an IRA (individual retirement account) with an APR of
8%.
At the end of each month he deposits
$45
in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
65 - 18 ==47 years
47 x 12 ==564 months
P=45; R=0.08/12; N=47*12; FV=P*((1 + R)^N - 1)/ R
FV = $279,556.98 - balance in his IRA account by age 65.
Total deposits made ==564 x $45 ==$25,380
$279,556.98 - $25,380 ==$254,176.98 - interest earned on his IRA over the period of 47 years.
Note: I took the interest rate of 8% as being compounded monthly.
