Smith borrows $30,000$ at an annual effective interest rate of $10\%.$ He agrees to

make annual payments at the end of each year for $9$ years, and an additional

balloon payment, X$,$ at the end of the tenth year. Each of the first $9$ payments

equals $25\%$ more than what is owed in interest at the time of the payment.

The balloon payment, X$,$ equals the amount needed to pay off the loan.

Determine X$.$

THe answer should be $26275\mathrm{.}7718$