Question

Frank purchased his house 16 years ago by taking out a 25-year mortgage for $150,000. The mortgage has a fixed interest rate of 5 percent compounded monthly. If he wants to pay off his mortgage today, how much money does he need? He made his most recent mortgage payment earlier today.

Answer 1

Calculation of Monthly Payment:

Loan Amount = $150,000
Period of Loan = 25 years or 300 months
Annual Interest Rate = 5%
Monthly Interest Rate = 5%/12 = 0.4167%

Monthly Payment * PVIFA(0.4167%, 300) = $150,000
Monthly Payment * (1 - (1/1.004167)^300) / 0.004167 = $150,000
Monthly Payment * 171.05323 = $150,000
Monthly Payment = $876.92

Calculation of Loan Amount due:

Period of Loan = 9 years or 108 months
Monthly Payment = $876.92
Monthly Interest Rate = 0.4167%

Amount due = $876.92 * PVIFA(0.4167%, 108)
Amount due = $876.92 * (1 - (1/1.004167)^108) / 0.004167
Amount due = $876.92 * 86.82465
Amount due = $76,138.27

So, Frank will need $76,138.27 to pay off remaining loan.