You are doing some bookkeeping concerning a mortgage you took out 10 years ago, $500,000 used...
You are doing some bookkeeping concerning a mortgage you took out 10 years ago, $500,000 used to finance a home. You presume it is a 30-year mortgage. You are trying to determine the interest rate (mortgage equivalent yield) on the loan. You know that the monthly payments are $4,023.11. So, you assume therefore that the interest rate on the loan is 9% and call your mortgage broker to check this out. Looking at your numbers, he tells you that you have two things incorrect. First, this was a weird mortgage that did not start with a 30-year maturity. Second, the 9%, it turns out, was purely coincidental. He also tells you that the actual interest paid thus far is 8.78% less than that shown in your calculations based on the 9% interest rate and a $500,000 loan – that is the interest paid is .9122 times the figure calculated from your mortgage calculation. From this information, can you determine the actual terms of the mortgage: rate and maturity?
Homework Answers
Interest rate on the loan: 8.5%
Maturity: 25 years
First, assuming 9% interest rate on a 30-year mortgage, I can use Excel to calculate howmuch interest I have paid in the past 10 years.
As you can see from the table, the total interest payment that I have made in the past 10 yearsis $429,922.52, assuming 9% interest rate on a 30-year mortgage.
Then, according my broker’s description, I can calculate my actual interest payment, whichis: 429,922.52 * 0.9122 = $392,175.32
Then, using Excel, I keep plugging in different interest rates into my formula until I get thetotal interest payment equals $392,175.32. Using this method, I figure out the interest rate onthe loan is 8.5% and the monthly rate is 0.7083%.
Then, I put monthly payment 4023.11 and monthly rate 0.7083% into the annuity formulaand solve for the maturity, getting the maturity is 300 months, which is equivalent to 25years.
Therefore, I know this is a 25-year mortgage with 8.5% annul interest
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