A bank features a savings account that has an annual percentage rate of $r=5\mathrm{.}3\%$ with interest compounded quarterly. Kimi deposits $$5,000$ into the account.

The account balance can be modeled by the exponential formula $A(t)=a(1+\frac{r}{k}{)}^{kt},$ where $A$ is account value after $t$ years, $a$ is the principal $($starting amount$),r$ is the annual percentage rate, $k$ is the number of times each year that the interest is compounded.

$($A$)$ What values should be used for $a,r,$ and $k?$

$a=,r=,k=$

$($B$)$ How much money will Kimi have in the account in $9$ years?

Answer $=$$

Round answer to the nearest penny.

$($C$)$ What is the annual percentage yield $($APY$)$ for the savings account? $($The APY is the actual or effective annual percentage rate which includes all compounding in the year$).$

APY$=,\%.$

Round answer to $3$ decimal places.