Question $6$

At the age of $23,$ Jordan decided to start saving for retirement $($at age $65).$ To meet his goal, Jordan decided to deposit $$370$ at the end of each month into his Roth $401k$ account that earns $9\mathrm{.}73\%$ interest, compounded monthly.

Determine the future value of the retirement account when Jordan retires at age $65.$ Round the solution to the nearest cent, if necessary.

Future Value $=$$

Determine the total amount of interest earned in Jordan's retirement account when Jordan retires at age $65.$ Round the solution to the nearest cent, if necessary.

Total Interest $=$$

Hint: Related Formulas

In the formulas below, A represents an account balance after $t$ years, where $P$ is the periodic payment made at the end of each compounding period, $r$ is the annual rate of interest $($in decimal form$),$ and $n$ is the number of compounding periods per year.

$A=\frac{P[(1+\frac{r}{n}{)}^{nt}-1]}{\frac{r}{n}},P=\frac{A(\frac{r}{n})}{[(1+\frac{r}{n}{)}^{nt}-1]}$