Question

Advanced Time Value of Money Problems

Question 2 (2nd mortgage problem)

You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.

1. What is the monthly payment?

2. During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?

3. How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?

4. How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal?

Answer 1

To find out the monthly payment we follow the following steps:

We are given the following information:

r	8.00%
n	30
frequency	12
PV	0.80 x 500000 = 400000

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

So the PMT is $2935.06

To find out the month in which the principal portion first exceed the interest portion, we need to create the following amortization schedule:

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Loan-Principal repayment
• PMT is calculated as per the above formula
• Interest = 0.08/12 x opening balance
• Principal repayment = PMT - Interest
• During the 257th month, the principal first exceeds the interest amount, the answer is not surprising because we don't see any discrepancy from a standard amortization pattern in which the interest goes on decreasing and the principal goes on increasing as we progress through the loan period
• Following is the graph for interest and principal payment
  • 
    

To find out how long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment, we need the following schedule:

• Keeping the monthly payment the same and adding an additional payment of 300 towards principal repayment, we get the above schedule
• Principal repayment = PMT - Interest+additional payment
• Due to additional principal repayment, the loan gets paid off in 262 months, in which the last payment is that of settling up the account and therefore lower than other payments

To find out how long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal, we need to create the following schedule:

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Loan-Principal repayment-additional payment
• Keeping the monthly payment the same and adding an additional payment equal to the principal repayment, we get the above schedule
• Due to additional principal repayment, the loan gets paid off in 181 months, in which the last payment is that of settling up the account and therefore lower than other payments