A small business takes out a loan of $12,000$ at a nominal rate of $12\%,$ compounded quarterly, to help finance its start$-$up costs. Payments of $750$ are

made at the end of every $6$ months for as long as is necessary to pay back

the loan.

Three months before the $9$th payment is due, the company refinances the

loan at a nominal rate of $9\%,$ compounded monthly. Under the refinanced

loan, payments of R are to be made monthly, with the first monthly payment

$37$ FINDING THE LOAN BALANCE USING PROSPECTIVE AND RETROSPECTIVE METHODS$\mathrm{.}3$to be made at the same time that the $9$th payment under the old loan was to

be made. A total of $30$ monthly payments will completely pay off the loan.

Determine R$.$