Ximena is trying to get a mortgage loan of $$170,000.$ The bank quotes her a $15-$year rate of $5\mathrm{.}6\%$ and a $30-$year rate or $7\mathrm{.}5\%.$ Both of these loans involve equal monthly payment.

a$.$ What is monthly payment for the $15-$year loan? What is the total interest paid?

b$.$ What is the monthly payment for the $30-$year loan? What is the total interest paid?

c$.$ What is the APR for each option?