Amanda Rice has just arranged to purchase a $$590,000$ vacation home in the Bahamas with a $25$ percent down payment. The mortgage has a $6\mathrm{.}5$ 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.