Problem $4-30$ Balloon Payments

Amanda Rice has just arranged to purchase a $$640,000$ vacation home in the Bahamas with a $20$ percent down payment. The mortgage has a $7$ percent APR compounded monthly and calls for equal monthly payments over the next $30$ years. Her first payment will be due one month from now. However, the mortgage has an eight$-$year balloon payment, meaning that the balance of the loan must be paid off at the end of Year $8.$ There were no other transaction costs or finance charges. How much will Amanda's balloon payment be in eight years? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Balloon payment