Question

You need a 25-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at an APR of 5.35 percent for this 300-month loan. However, you can afford monthly payments of only $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 $800

Answer 1

409,461.10

Step-by-step explanation:

Present value = Annuity value * [1 - (1/(1+r)^r)] / r

Present value = 800 * [1 - (1/(1+0.0535/12)^25*12)}/0.0535/12

Present value = 132196.0205

Remaining balance = Total loan - Present value of monthly payments = 240,000 - 132196.0205 = 107803.9795

Future value = Cash flow * [1 + Interest rate/Number of months)^Time period

Future value = 107803.9795*[1+0.0535/12]^360

Future value = 409,461.10

Note: Balloon payment mean final payment made by the borrower after the end of partial amortization over the time period of the mortgage