Question

You need a 35-year, fixed-rate mortgage to buy a new home for $310,000. Your mortgage bank will lend you the money at an APR of 6.05 percent for this 420-month loan. However, you can afford monthly payments of only $1,500, 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 $1,500?

Answer 1

Solution and explanation

Present value of the $1,500 monthly payments is  

PMT                                                                                       $1,500

Annual Rate                                                                               6.05%

Number of period (NPER)                                                        420

Present value Annuity (PVA) (calculated in excel using PV function)                                 $261,528.41

$\mathrm{PVA}=\ 1,500\left[\left(1-\left\{1 /[1+(.0605 / 12)]^{\wedge} 420\right\}\right) /(.0605 / 12)\right]$ $261,528.41  

Cost of Home                                                                          $310,000

Amount of principal still owe = $310,000 - $261,528.41 $48,471.59

Balloon payment in 35 years, which is the FV of the remaining principal =  

Present Value                                                            $48,471.59

Annual Rate                                                                      6.05%

Number of period (NPER)                                              420

Future Value (calculated in excel using FV function) $400,677.90

Balloon payment = $\mathbf{S} 48,471.59[1+(.0605 / 12)] 420$   $400,677.90