Question

# You need a 20-year, fixed-rate mortgage to buy a new home for \$190,000. Your mortgage bank...

You need a 20-year, fixed-rate mortgage to buy a new home for \$190,000. Your mortgage bank will lend you the money at a 8.6 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?

My options are

81324.59

437840.69

469437.44

451382.15

64640.23

Rate = 8.6% / 12 = 0.716667%

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

Present value = 950 * [1 - 1 / (1 + 0.00716667)240] / 0.00716667

Present value = 950 * 114.39514

Present value = \$106,675.3833

Remaining amount today = \$190,000 - \$106,675.3833 = \$81,324.6167

Future value = Present value * (1 + r)n

Future value = 81,324.6167 * (1 + 0.00716667)240

Future value = 81,324.6167 * 5.550382

Future value = \$451,382.15

Balloon payment will be \$451,382.15

Note: there might be some difference in decimals due to rounding issues.

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