Question

# Amanda Rice has just arranged to purchase a \$530,000 vacation home in the Bahamas with a...

 Amanda Rice has just arranged to purchase a \$530,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 5.9 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?

 Loan amount = Value of home * ( 1 - Downpayment % ) = 530000 * ( 1 - 20% ) = 424000 n = Total mortgage months = 30 * 12 = 360 r = Rate per month = 5.9% / 12 Monthly mortgage payment = Loan amount / ( (1-(1+r)^-n)/r ) = 424000 / ( (1-(1+5.9%/12)^-360)/(5.9%/12) ) = 2514.90 After 8 years : n = Months left = 360 - ( 8 * 12 ) = 264 r = Rate per month = 5.9% / 12 Balloon payment = Monthly mortgage payment * (1-(1+r)^-n)/r = 2514.90 * (1-(1+5.9%/12)^-264)/(5.9%/12) = 371379.64

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