The Taylors agreed to monthly payments rounded up to the nearest $$100$ on a mortgage of $$336,000\mathrm{.}00$ amortized over $15$ years. Interest for the first five years was $2\mathrm{.}5\%$ compounded semi$-$annually. Determine the mortgage balance at the end of the five$-$year term. Hint: First, determine the required monthly mortgage payment and then round that payment up to the nearest $$100.$ Second, recalculate N$.$ a$.$

$$102,384\mathrm{.}77$

b$.$

$$265,785\mathrm{.}36$

c$.$

$$107,755\mathrm{.}64$

d$.$

$$233,657\mathrm{.}28$

e$.$

$$220,384\mathrm{.}77$