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Five years ago, Diane secured a bank loan of $$360,000$ 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 $5\frac{\%}{?}$ year compounded monthly on the unpaid balance. Because the interest rate for a conventional $30-$year home mortgage has now dropped to $1\mathrm{.}5\frac{\%}{?}$ year compounded monthly, Diane is thinking of refinancing 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 $1\mathrm{.}5\frac{\%}{?}$ year compour monthly, what will be her monthly mortgage payment?

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

$ $$

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