$4.$ Paul and Evelyn Peters were $$house hunting$$ five years ago when mortgage rates were pretty high. The fixed rate they could get on a $30-$year mortgage was $4\mathrm{.}75\%$ while the $15$ year fixed rate was at $4\%.$ After looking at many houses, they decided to buy a $$300,000$ two$-$story townhome in the Midwest, and to avoid paying PMI, they borrowed from family members and friends and collected the $20\%$ down payment. Since they already had significant credit card debt, and student loans they were paying off, Evelyn and Paul decided on the $30-$year mortgage even though the interest rate is higher.

a$.(1$ point$)$ How much is Paul and Evelyn$$s Mortgage payment per month?

b$.(4$ points$)$ Prepare an amortization table for the $30$ year loan, and calculate how much of their mortgage principal they have paid down and how much of their interest?

c$.(1$ point$)$ What would have been their monthly mortgage payment, had they taken the $15$ year loan? How much more per month?

$5.$ Paul and Evelyn$$s house $($from previous question $)$ has gone up in value over the last $5$ years and is now worth $$425,000.$ Since interest rates have also decreased in the last few years, Paul and Evelyn now have offers to refinance their mortgage.

a$.(1$ point$)$ What would the new monthly payments be for the Peters$$ if they choose to refinance the mortgage?

b$.(4$ points$)$ How much would they save in interest payments over the remaining life of their loan? Should they refinance? $($hint: you may need to do another amortization table for the new loan$)$

c$.(4$ points$)$ The lenders are also giving Paul and Evelyn the option to cash out some of the equity on their house. They can borrow up to $80\%$ of the new appreciated home value. How much can they cash out? If they choose to cash out, what would the monthly payments on their refinance loan be$?$ Should they cash out given the returns on most investments are currently $6\%$ a year?