The Smiths are refinancing their home mortgage to a $15-$year loan at $3\mathrm{.}6\%$ annual interest compounded monthly.

Their outstanding balance on the loan is $$170,000.$

$($a$)$ Under their current loan, the Smiths' monthly mortgage payment is $$1588.$ How much will the Smiths be saving in

their monthly mortgage payments by refinancing?

$($b$)$ How much interest will the Smiths pay over the life of the new loan?

$($a$)$ The Smiths' will save $ a month in their monthly payment.

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