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Questions on Mortgage Math

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Posted On: 11/26/2014

Question: You recently said a borrower could save $840 by taking $20,000 in retirement funds and using the money to reduce the size of a fixed-rate, 30-year mortgage at 4.2 percent. However, over the life of a $280,000 loan the interest savings are only about $15,208 when compared with a $300,000 mortgage. That’s about $42 per month ($15,208 divided by 360 = $42.24). How is the borrower saving $840 per year?

Answer: If you have an annual return of 4.2 percent on $20,000 you get $840 per year.

Using an amortization calculator we can see that:

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A $300,000 loan over 30 years at 4.2 percent has a total potential interest cost of $228,138. The monthly payment for principal and interest is $1,467.05

A $280,000 loan – $300,000 less $20,000 – has a lifetime interest cost of $212,930 at 4.2 percent. The monthly payment for principal and interest is $1,369.25.

The difference between the two payments is $97.80 per month or $1,174 per year. As it happens, $97.80 per month is what you would pay to borrow $20,000 over 30 years at 4.2 percent.

In practice, there are several points.

First, Freddie Mac says the typical loan at this time is refinanced after 7.34 years. For this reason annual cash savings are likely to be a more important issue for most borrowers than lifetime potential interest decreases.

Second, the $20,000 mortgage balance reduction does not “earn” $840 in the sense of interest or dividends. The $840 is a “savings,” and we do not tax savings.

Third, with a fixed-rate loan the total monthly payment for principal and interest is the same for the life of the loan. What changes is the composition of the payment. Each month you pay a little less interest and a little more principal until the loan is paid off. Your principal balance is being converted into real estate equity and hopefully the equity in your home will go up over time as home prices increase and loan balances are paid down.

Fourth, with ARMs the situation is different because interest rates and monthly payments can rise and fall. We have no way to predict how monthly costs might change, other than to say that future interest rate changes are capped to fit within whatever limits have been established by the ARM loan contract.

Fifth, with retirement funds getting so little return today some borrowers might be better off using the money to hold down mortgage expenses.

Which borrowers? As the original column said, “it may be neither easy nor desirable to get retirement money. Before looking at homes find out if you have the right to withdraw funds from your account. Is there a limit on the amount you can withdraw? How long does it take to get the money? How will your withdrawal be treated for tax purposes? Will you have to pay a penalty? For specifics regarding these and other questions speak with your account adviser and a tax professional.”

Peter G. Miller is the author of The Common-Sense Mortgage and a veteran real estate columnist. Have a question? Please write to peter@ctwfeatures.com.

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