Problem: You're purchasing a home which is listed at $$400,000.$ You plan to make a down

payment of $10\%$ of the home's value $($$$40,000)$ and securing a mortgage to cover the remaining

principal and closing cost. The mortgage, offered by Chase, is for $30$ years and carries an interest

rate of $7\mathrm{.}75\%,$ with payments due monthly. Additionally, your mortgage entails a one$-$time

closing cost $($appraisal fees, title insurance, etc.$)$ equivalent to $5\%$ of the mortgage value.

Part A:

$1)$ What would be the total value of your mortgage that you need to get from Chase?

$2)$ What would be your monthly payment?

$3)$ How much is the total value of the interest you pay for your mortgage on top of the

principal?

$4)$ How would the results for parts $1-3$ change if you decide to make a down payment of

$20\%$ of the home$$s value?

Part B:

Assume after $10$ years, Federal Reserve implements a new policy to stimulate economic

growth by lowering interest rate. As a result, you explore the option of refinancing your

mortgage to secure a more favorable rate. PNC Bank offers you $6\%$ interest rate, however the

refinancing cost and closing cost $($one$-$time payment$)$ together would be now $7\%$ of the value of

your new mortgage. Will you accept the offer and refinance your mortgage?

To determine whether you should accept this offer and refinance your mortgage, answer

to the following questions:

$5)$ How much is the remaining principal from your original mortgage at year $10?$

$6)$ How much would be the total amount you need to refinance with your new mortgage $($the

remaining principal of your original mortgage plus $7\%$ one$-$time payment$)$

$7)$ What would be your monthly payment for the next $20$ years with $6\%$ interest rate?

$8)$ Compare the answer in part $(7)$ vs$.$ part $(1).$ Will you be willing to refinance your

mortgage?