Question

# You need a 25-year, fixed-rate mortgage to buy a new home for \$190,000. Your mortgage bank...

 You need a 25-year, fixed-rate mortgage to buy a new home for \$190,000. Your mortgage bank will lend you the money at a 9.1 percent APR 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?

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Mortgage = 190,000

Rate per period = 0.091 /12 = 0.00758333333

Monthly payment = 800

Now mortgage = Present value of Monthly payment + Present Value of Balloon Payment

190,000 = 800 * PVAF (0.00758333333, 1 - 300 months) + Balloon Payments * PVF (0.00758333333, 300th months)

190,000 = 800 * 118.19565125607 + Balloon Payments * 0.10368297836

190,000 = 94556.5210048 + Balloon Payments * 0.10368297836

Balloon Payments = 190,000 - 94556.5210048 / 0.10368297836

Balloon Payments = 920531.80

PVAF = 1- (1/ (1+r)^n) / r

PVF = 1 / (1+r)^n

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