A borrower takes out a loan to be repaid over $20$ years. The first payment is $1,102$ payable at the end of the first month. Each

subsequent monthly payment is five more than the previous month's payment.

Calculate the accumulated value of the payments at the end of $15$ years using an annual effective interest rate of $6\mathrm{.}5\%.$

$442,031$

$443,525$

$445,578$

$447,287$

$448,547$