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.

If you choose to repay the borrowing in equal installments monthly over a $20$ years, what would be the difference between your monthly payments at the two different APRs?

a$.$

$$26\mathrm{.}98$

b$.$

$$68\mathrm{.}94$

c$.$

$$154\mathrm{.}58$

d$.$

$$89\mathrm{.}32$