Assume you plan to borrow $$400,000$ from your bank to buy a home. The bank offers:

a $5-$year fixed rate of $6\mathrm{.}05\%,$ compounded monthly.

a $3-$year fixed rate of $5\mathrm{.}75\%,$ compounded monthly.

You expect that the interest rate will decrease in the near future, therefore you eventually choose the $3-$year fixed rate. Then, what will be your mortgage balance after $3$ years?

a$.$

$$379,325\mathrm{.}89$

b$.$

$$321,598\mathrm{.}59$

c$.$

$$365,056\mathrm{.}12$

d$.$

$$452,321\mathrm{.}21$