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?