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