Phil secures a $$350,000,15-$year mortgage with an annual interest rate of $5\mathrm{.}5\%.$ What will be the unpaid principal balance on Phil's mortgage at the end of $10$ years?

A$)$

$$200,281\mathrm{.}78$

B$)$

$$168,128\mathrm{.}00$

C$)$

$$145,238\mathrm{.}22$

D$)$

$$149,718\mathrm{.}22$