Problem $7\mathrm{.}8$

You are looking to purchase a Tesla Model $x$ sport utility vehicle. The price of the vehicle is $$96,750.$ You negotiate a six$-$year loan, with no money down and no monthly payments during the first year. After the first year, you will pay $$1,625$ per month for the following five years, with a balloon payment at the end to cover the remaining principal on the loan. The APR on the loan with monthly compounding is $5\mathrm{.}4$ percent. What will be the amount of the balloon payment six years from now?

Note: Do not round monthly interest rate calculation. Round intermediate value calculation and final answer to $2$ decimal places.

Amount of balloon payment