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.
