Suppose Sierra would like to retire in $36$ years with a retirement account balance of $$1,000,000.$ To this end, Sierra plans to make a periodic payment at the end of each month for $36$ years into her Roth IRA account that earns $5\mathrm{.}65\%$ interest, compounded monthly.

Determine the periodic payment required that Sierra needs to deposit at the end of each month. Round the solution to the nearest cent, if necessary.

Periodic Payment $=$$

Determine the total amount deposited by Sierra in this account over the $36$ years. Round the solution to the nearest cent, if necessary.

Total Deposits $=$$

Determine the total amount of interest earned in this account over the $36$ years. 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.

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