Question

11. Andrew is planning for retirement, and he estimates that he'll want to be able to withdraw $1,500 each week for 15 years once he retires. He opens a Roth IRA and finds investments that he expects to return 3.45% interest compounded weekly.(a) How much will he need to have in the account when he retires in order to meet his goal? $(b) How much will he have to deposit each week for the next 40 years in order to get this balance at retirement? $(c) How much interest will his deposits earn between now and retirement? $

Answer 1

Consider that the principal (P) invested at an annual rate of interest (R) for time (T) compounded as per the number of periods (n), gives an amount (A) of,

$A=P(1+\frac{R}{n})^{nT}$

The corresponding interest is given by,

$\begin{gathered} CI=A-P \\ CI=P(1+\frac{R}{n})^{nT}-P \end{gathered}$

According to the given problem,

$\begin{gathered} CI=1500 \\ T=15 \\ R=3.45\text{ percent}=0.0345 \\ n=52 \end{gathered}$

Substitute the values,

$\begin{gathered} 1500=P(1+\frac{0.0345}{12})^{52\cdot15}+P \\ 1500=1.5126P+P \\ P=\frac{1500}{2.5126} \\ P\approx596.979 \end{gathered}$