Question

Lisa is $21$ years old and starting an IRA (individual retirement account).

She is going to invest $\$50$ at the beginning of each month.

The account is expected to earn $2.5\%$ interest, compounded monthly.

How much money, rounded to the nearest dollar, will Lisa have in her IRA if she wants to retire at age $52$?

• A. $\$28,052$
• B. $\$28,111$
• C. $\$40,676$
• D. $\$40,731$

Answer 1

The correct option is B

$\$28,111$

Calculate Future Value of Annuity Due:

Future Value of Annuity Due is defined as:

$P\left[\frac{{\left(1+r\right)}^n-1}{r}\right]\times \left(1+r\right)$

Here, $P$ is Periodic payment, $r$ is the rate per period, $n$ is the number of periods.

The following values are given as:

$P=\$50$, $r=\frac{0.025}{12}$, $\begin{array}{rcl}n& =& 31\times 12=372\end{array}$

Substitute the above values in the formula to find the future value:

$\begin{array}{rcl}\text{Future Value of Annuity Due}& =& 50\left[\frac{{\left(1+{\displaystyle \frac{0.025}{12}}\right)}^{372}-1}{{\displaystyle \frac{0.025}{12}}}\right]\times \left(1+\frac{0.025}{12}\right)\\ & \Rightarrow & =28110.67\\ & \Rightarrow & \approx \$28111\end{array}$

Therefore, Lisa will have $\mathbf{\$}\mathbf{28111}$the amount in her IRA.