Stefan finished his college program on June $3$ with Canada Student Loans totalling $$12,490.$ He decided to capitalize the interest that accrued $($at prime plus $2\mathrm{.}5\%)$ during the grace period. Upon consolidation, he chose the floating rate option of prime $+2\mathrm{.}5\%.$ Stefan$$s first end$-$of$-$month payment of $$275$ was made on January $31.$ The prime rate on June $3$ was $3\mathrm{.}75\%,$ increased to $3\mathrm{.}85\%$ effective August $8,$ and increased again to $4\mathrm{.}05\%$ effective January $5.$ Calculate the balance owed on the loan after the January $31$ payment. $($Use $365$ days a year. Do not round intermediate calculations. Round your final answer to $2$ decimal places.$)$