The Taylors agreed to make monthly payments on a mortgage of $$127,000$ amortized over $15$ years. Interest for the first $3$ years was $7\mathrm{.}5$ percent compounded semi$-$annually. Determine the mortgage balance at the end of the $3-$year term.

A$.$ $$111,680\mathrm{.}73$

B$.$ $$111,440\mathrm{.}09$

C$.$ $$188,860\mathrm{.}05$

D$.$ $$188,018\mathrm{.}17$