A family takes out a mortgage for $$293,900\mathrm{.}00$ from the local bank. The loan is for $30$ years of monthly payments at a $3\mathrm{.}72\%$ APR $($monthly compounding$).$ What will the family's balance be on the mortgage after $9\mathrm{.}50$ years?

Answer format: Currency: Round to: $2$ decimal places.