$1.($a$)$ If you deposit $$12,000$ in the bank today, what is its future value at the end of thirteen years if it is invested in an account paying $6\mathrm{.}24\%$ interest $($annual compounding, or APR$)?$

$($b$)$ What is the present value of $$12,000$ to be received in thirteen years if the appropriate interest rate is $6\mathrm{.}24\%$ APR, continue to assume annual compounding?