Utilizing Exhibit $7-7$ in the textbook on page $231,$ answer the following questions:

$[$Make sure to show your work$]$

a$.$ Calculate the monthly mortgage payment for a $$200,000,30-$year loan at a $3\mathrm{.}0\%$ term rate $($which was the rate in April $2021).$

b$.$ Calculate the monthly mortgage payment for a $$200,000,30-$year loan at a $7\mathrm{.}0\%$ term rate $($which was the rate in April $2023).$

c$.$ The term rates have more than doubled in the past $3$ years. How has that affected the monthly mortgage payments for parts a and $b?$ Explain how this will have likely affected people's ability to even purchase an inexpensive home.