Question

You deposit $ 142 each year into an IRA earning 4.6 % interest compounded annually. How much will you have in the account in 18 years?

Answer 1

We have to calculate the future value (FV) after n = 18 years of an investment of $142 each year, with a rate of interest of 4.6% (r = 0.046) compounded annually.

We can calculate the future value of an annuity like this as:

$FV=P\cdot\frac{(1+r)^n-1}{i}$

Replacing and calculating, we get:

$\begin{gathered} FV=142\cdot\frac{(1+0.046)^{18}-1}{0.046} \\ FV=142\cdot\frac{1.046^{18}-1}{0.046} \\ FV\approx142\cdot\frac{2.24683-1}{0.046} \\ FV\approx142\cdot\frac{1.24683}{0.046} \\ FV\approx142\cdot27.1 \\ FV\approx3848.91 \end{gathered}$

Answer: She will have $3848.91 in her account.