Five years ago, Diane secured a bank loan of $$320,000$ 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 $5\mathrm{.}5\%$ 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 $5\mathrm{.}5\%$ year compounded monthly, what will be her monthly mortgage

payment?

$

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

$