After $5$ years, you decide not to use the money for a car. Instead, you'll take $$10,000$

of it to buy a house. You find a home you love for $$375,000.$

a$.$ Assuming that you get an interest rate of $5\mathrm{.}75\%,$ plan on taking about a $30-$

year mortgage, and you will put a down payment of $$8,000,$ what will your

monthly payment be$?($hint: find PMT$,$ and don't forget to take out the down

payment!$)$

b$.$ Yikes! That payment is way too much! You want to have a mortgage payment

of $$1200.$ Assuming that you get an interest rate of $5\mathrm{.}75\%,$ plan on taking about a

$30-$year mortgage, and a payment of $$1200$ each month, how big of a mortgage

should you get? $($hint: find PV$.$ Do NOT take out a down payment.$)$

c$.$ After your findings in $5$ b$,$ you aim for a $$200,000$ mortgage. Assuming you get

an interest rate of $5\mathrm{.}75\%,$ plan on taking about a $30-$year mortgage, and the

mortgage is $$200,000,$ how much will you pay over the life of the mortgage?

$($hint: find the PMT first$)$

d$.$ How much of that was interest if the loan was $$200,000?($hint: use the PMT

and PV$)$

e$.$ How much money could you have saved if you did a $15-$year mortgage

instead? $($hint: rerun the TVM$)$