Audrey sanborn has just arranged to purchase a $450,000 vacation home in the bahamas with a 20 percent down payment. the mortgage has a 7.5 percent stated annual interest rate, 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 audrey’s balloon payment be in eight years?

Aubrey pays 20% of the cost upfront, which means her loan amount will be 360,000. The formula to calculate her monthly payment is Payment = Principal x (r) / (1-(1+r)^n), where r is the monthly rate of interest (7.5%/12=.63%), and n is the number of terms (30*12=360). The calculation yields a monthly payment of 2517.17. We can find the present value of the first 96 payments (12 x 8) to find how much principle will be paid down, and what the balloon payment will need to be to pay off the rest of the principle.

The Remaining balance of a loan is found through the following calculation: PV(1+r)^n – (P(1+r)^n)-1))/r where PV is the initial loan amount, P is the monthly payment 2515.17, n is 96 and r is .0063, the monthly rate. This calculation gives us roughly $325,001 remaining on the loan after 8 years, so this will be the balloon payment.