Question

# You need a 20-year, fixed-rate mortgage to buy a new home for \$220,000. Your mortgage bank...

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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