A friend borrows $$17725\mathrm{.}09$ from you with an annual effective interest rate of $i=8\mathrm{.}5\%.$

They intend to repay the loan through $49$ payments. The first $48$ are monthly payments

of $$426\mathrm{.}75$ each, made at the end of every month starting at the end of the first month.

The last payment, of $$426\mathrm{.}75,$ is made after the $48$ th payment. Find the time of the

$49$th payment?