You need a 35-year, fixed-rate mortgage to buy a new home for $340,000. Your mortgage bank will lend you the money at an APR of 6.35 percent for this 420-month loan. However, you can afford monthly payments of only $1,800, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,800?

$338,712

Explanation:

we must first calculate the monthly payment using the present value of an annuity formula:

present value = monthly payment x annuity factor

present value = $340,000

PV annuity factor, 0.529167%, 420 periods = 168.38268

monthly payment = $340,000 / 168.38268 = $2,019.21

Since the monthly payment was actually higher than $1,800, the balloon payment will be almost $340,000

I prepared an amortization schedule using an excel spreadsheet. During the first years, the principal is only decreasing by $1 each month

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%