Assume that there are $200$ buyers with the following ability to make monthly payments

$1.50$ buyers $-$ $$3,000$

$2.50$ buyers $-$ $$2,500$

$3.50$ buyers $-$ $$2,000$

$4.50$ buyers $-$ $$1,500$

a$)$ What is the monthly mortgage payment for a home that costs $$500,000,20\%$ downpayment, $6\%$ interest rate, $30$ years fixed payment? $($Round your answer to the second decimal point.$)$

b$)$ How many total buyers can afford homes based on the monthly mortgage payment in this case?

c$)$ What is the monthly mortgage payment for a home when the interest rate is $8\%($everything else equal$)?($Round your answer to the second decimal point.$)$

d$)$ How many total buyers can afford homes based on the monthly mortgage payment in this case?

e$)$ How many total buyers can afford homes when the interest rate is $8\%$ but they can put $40\%$ downpayments