Alysha would like to borrow $$45,000$ to pay one year$$s tuition at a private U$.$S$.$ university. She would like to make quarterly payments and finish repaying the loan in $5$ years. If the bank is quoting her a rate of $4$ percent compounded monthly, determine her quarterly payment. $($Round effective interest rate to $4$ decimal places, e$.$g$.25\mathrm{.}1253\%$ and final answer to $2$ decimal places, e$.$g$.125\mathrm{.}12.)$