Suppose Constanza would like to accumulate $$452,000$ for a personal goal. To this end, Constanza plans to make a periodic payment at the end of each six$-$month period for $14$ years into an account that earns $8\mathrm{.}3\%$ interest, compounded semi$-$annually.

Determine the periodic payment required, $P,$ that Constanza needs to deposit at the end of each six$-$month period. Round the solution to the nearest cent, if necessary.

Periodic Payment $=$$

Determine the total amount deposited by Constanza in this account over the $14$ years. Round the solution to the nearest cent, if necessary.

Total Deposits $=$$

Determine the total amount of interest earned in this account over the $14$ 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.

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