Sam is considering investing in a bond with a face value of $$20,000.$ The bond pays an interest of $4\%($per annum$)$ payable quarterly. If he expects to make a $1(1)/(2)\%$ return per quarter compounded quarterly on this investment with a maturity of $20$ years, determine the most he is willing to pay for the bond $\_\_\_\_\_\_\_\_.$

Group of answer choices

$$18,102\mathrm{.}65$

$$14,923\mathrm{.}86$

$$15,355\mathrm{.}40$

$$16,000\mathrm{.}00$