Suppose you want to buy a $$142,000$ home. You found a bank that offers a $30-$year loan at $4\mathrm{.}5\%$ APR.

What will be your monthly payment? $($Round to the nearest cent.$)$

$

How much would you end up paying the bank for the home after $30$ years? $($Round to the nearest cent.$)$

$

Suppose you wanted to reduce the time of your loan to $25$ years. What would be your new monthly payment?

$($Round to the nearest cent.$)$

$

How much would you end up paying the bank for the home after $25$ years? $($Round to the nearest cent.$)$

How much did you save by reducing the time of your mortgage loan? $($Round to the nearest cent.$)$