Question

Seven years ago, Emmanual purchased a beautiful new home. He financed the acquisition with a 30-year mortgage. The original loan amount was $185,000, and the rate on the mortgage was 5.6 percent per year (compounded monthly). The mortgage requires monthly payments. Today, Emmanuel decided he wants to pay off the loan.  What is the current outstanding balance on this mortgage? (Assume the mortgage has 23 years remaining, and the next payment is due in one month.)

Answer 1

We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	5.60%
Number of years	n	30.00
Monthly compounding	frequency	12.00
Loan amount	PV	185000.00

We need to solve the following equation to arrive at the required PMT:

So the monthly payment is 1062.05

We now create the amortization schedule:

• Opening balance = previous year's closing balance
• Closing balance = Opening balance-Principal repayment
• PMT is calculated as per the above formula
• Interest = 0.056 /12 x opening balance
• Principal repayment = PMT - Interest
• So if 23 years are remaining then 7 years have completed and that iplies 7x12 = 84 payments have completed
  • So we need to see the closing balance after the 84th payment in the above schedule, which is  $164,621.06 so this is our answer.