Five years ago, Diane secured a bank loan of $$330,000$ 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 $9\%/$year$,$ compounded monthly on the unpaid balance.

Because the interest rate for a conventional $30-$year home mortgage has now dropped to $6\mathrm{.}5\%$ year, compounded monthly, Diane is thinking of refinancing her property. $($Enter

your answers in dollars and cents. 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

$6\mathrm{.}5\frac{\%}{?}$ year, compounded monthly, what will be her monthly mortgage payment?

$

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

$