You need a 20-year, fixed-rate mortgage to buy a new home for $220,000. Your mortgage bank will lend you the money at a 6.6 percent APR for this 240-month loan. However, you can afford monthly payments of only $950, 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 $950?
Cost of house = $220,000
Monthly payment = $950
Annual interest rate = 6.60%
Monthly interest rate = 0.55%
Number of payments = 240
Present value of monthly payments = $950/1.0055 + $950/1.0055^2
+ ... + $950/1.0055^239 + $950/1.0055^240
Present value of monthly payments = $950 * (1 - (1/1.0055)^240) / 0.0055
Present value of monthly payments = $950 * 133.07214
Present value of monthly payments = $126,418.53
Amount of principal paid on the loan = $126,418.53
Amount of principal remaining = Amount borrowed - Amount of
principal paid on the loan
Amount of principal remaining = $220,000 - $126,418.53
Amount of principal remaining = $93,581.47
Balloon payment = Future value of the principal remaining
Balloon payment = $93,581.47 * 1.0055^240
Balloon payment = $93,581.47 * 3.72991
Balloon payment = $349,050.46
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