What is the present value of the savings between a thirty$-$year mortgage that has an interest rate of $9\%$ and one that has an interest rate of$10\%?($Assume that payments are made at the end of the year and assume a discount rate of $9\%).$ You must find the present value of the difference between the payments you would make on the $10\%$ mortgage and the $9\%$ mortgage.

$-$$$17,964\mathrm{.}31$

$-$$$16,765\mathrm{.}32$

$-$$$1,748\mathrm{.}58$

$-$$$52,457\mathrm{.}40$