Question

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

Answer 1

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.