Problem $41\mathrm{.}21$

Betty borrows $19,800$ from Bank $x.$ Betty repays the loan by making $36$ equal payments of principal at the end of each month. She also pays interest on the unpaid balance each month at a nominal rate of $12\%,$ compounded monthly.

Immediately after the $16$ th payment is made, Bank $x$ sells the rights to future payments to Bank $Y.$ Bank $Y$ wishes to yield a nominal rate of $14\%,$ compounded semi$-$annually, on its investment.

What price does Bank $x$ receive?