What's the present value of $$20,000$ discounted back $5$ years if the appropriate interest rate is $4\mathrm{.}5\%,$ compounded semiannually?

Select the correct answer.

a$.$ $$16,034\mathrm{.}20$

b$.$ $$16,022\mathrm{.}20$

c$.$ $$16,058\mathrm{.}20$

d$.$ $$16,010\mathrm{.}20$

e$.$ $$16,046\mathrm{.}20$