Five years ago, Diane secured a bank loan of $$310,000$ 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 $5\mathrm{.}5\%/$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?

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

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$($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?

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

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