Hector has taken out a loan totalling $$13,000$ for an app for his business. The loan will be repaid by making end of quarter payments of $$405\mathrm{.}71$ for the next $10$ years. If interest is $4\mathrm{.}5\%$ compounded monthly, find the balance on the loan at the end of the $5$ th year? Enter your answer rounded to two decimal places.

Balance at the end of the $5$ th year: $