Question

Audrey Sanborn has just arranged to purchase a $550,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 6.1 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?

Answer 1

So in effect, we want to find the outstanding balance of the mortgage after 8 years.

original mortgage = .8(550,000) = 440,000
i = .061/12 = .00508333...
P(1 - 1.0050833..^-360)/.00508333.. = 440000
p(165.01792..) = 440000
p = 2666.38

After 8 years, outstanding balance
= balloon payment
= 440000(1.0050833..)^96 - 2666.38(1.0050833..^96 - 1)/.0050833..
I got $ 386,994.15

check my arithmetic