A family needs to take out a $30-$year home mortgage loan of $ $160000$ through a local bank. Annual interest rates for $30-$year mortgages at the bank are $3\mathrm{.}3\%$ compounded monthly.

$($a$)$ Compute the$$ family's monthly mortgage payment under this loan.

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