Suppose you purchased a house $3$ years ago and took out a mortgage for $$200,000$ with a $7\mathrm{.}5\%$ interest rate. The

mortgage is a $30$ year mortgage with monthly payments. Today you can refinance the loan at a $6\mathrm{.}5\%$ interest rate

for a fee of $$7,500.$ Assume that you would only refinance enough to repay the old loan and the cost of

refinancing.

A $-$ If you refinance by taking a new $30$ year loan at the new rate, how much will you save per month?

Monthly Savings

B $-$Should you refinance today?

Tip: Use the best interest rate available to you to determine the PV$.$

C $-$ If you expect to move in $3$ years, would you want to refinance?

Tip: You will have to make payments for the years until you move then pay whatever loan

balance is left. So consider what the difference in both payments and future value will be$.$