Suppose Rachel and Nadia buy a house and have to take out a loan for $$191000.$ If they qualify for an APR of $4\mathrm{.}25\%$ and choose a $30$ year mortgage, we can find their monthly payment by using the PMT formula. If Rachel and Nadia decide to pay $$1500$ per month, we can use goal seek to see how many years it will take to pay off the loan.

Use the PMT function and goal seek $($as needed$)$ to answer the following questions about Rachel and Nadia's mortgage.

a$.$ What is their monthly payment on the $30$ year loan?

$

b$.$ If they qualify for the same APR on a $15$ year loan, what will the new monthly payment be$?$

$

c$.$ If Rachel and Nadia have monthly payments of $$1500$ each month, how long will it take for them to pay off their loan?

years

d$.$ If they want to have monthly payments of $$650$ and still pay the loan off in $30$ years, what interest rate would they have to qualify for?

$\%$