You would like to have $$4,500$ in $3$ years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays $4\%$ compounded semiannually.

a$.$ Use one of the formulas below to determine how much you should deposit at the end of every six months.

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

b$.$ How much of the $$4,500$ comes from deposits and how much comes from interest?

a$.$ In order to have $$4,500$ in $3$ years, you should deposit $$714$ at the end of every six months.

$($Do not round until the final answer. Then round up to the nearest dollar.$)$

b$.$ $ $$ of the $$4,500$ comes from your deposits and $ $q,$ comes from interest. $($Use the answer from part a to find this answer. Round to the nearest dollar as needed.$)$