Five years ago, Diane secured a bank loan of $$340,000$ to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was $30$ years, and the interest rate was $8\%/$year compounded monthly on the unpaid balance. Because the interest rate for a conventional $30-$year home mortgage has now dropped to $4\mathrm{.}5\%/$year compounded monthly, Diane is thinking of refinancing her property. $($Round your answers to the nearest cent.$)$

$($a$)$ What is Diane's current monthly mortgage payment?

$

$($b$)$ What is Diane's current outstanding principal?

$

$($c$)$ If Diane decides to refinance her property by securing a $30-$year home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of $4\mathrm{.}5\%/$year compounded monthly, what will be her monthly mortgage payment?

$

$($d$)$ How much less will Diane's monthly mortgage payment be if she refinances?

$