“I see where Fannie Mae is test-marketing 40-year mortgages through a group of credit unions. Do you see the 40-year mortgage as a useful option for borrowers?”

No. While 40-year mortgages increase affordability by reducing the mortgage payment, the reduction is very modest. Furthermore, a small tweaking in the 30-year mortgage would accomplish the same thing, maybe better.

Arithmetic of Term Reduction: The impact of an extension in term on the mortgage payment is smaller the longer the initial term. At 6 percent interest, extending the term from 10 years to 20 reduces the monthly payment by 35.5 percent. Extending it further to 30 years reduces the payment by 16.3 percent. And going to 40 years reduces it by only 8.2 percent.

Even 8.2 percent is an exaggeration because lenders will set a rate at least 1/4 percent higher on 40-year than on 30-year mortgages. With a 1/4 percent increment, the payment reduction falls to 5.3 percent.

If market interest rates escalate, the bang from going to 40 years weakens even more. At 10 percent, for example, going from 30 to 40 years reduces the payment by only 3.2 percent, and if the 40-year is priced 1/4 percent higher, the reduction falls to 1 percent.

30-Years With a Residual Balance: A Better Option? If you take a 40-year loan of \$100,000 at 6 percent, your payment is \$550.21, and after 30 years you still owe \$49,553. A 30-year loan could be written for the same amount and rate, and with a payment of \$550.21, provided that a balance of \$49,553 was payable after 30 years. This could be called a “residual balance mortgage.”

The 40-year loan and the 30-year residual balance loan amortize in exactly the same way. The only difference between them is that in the second case the balance after 30 years must be repaid or refinanced.

This should make the residual balance mortgage more attractive to lenders because of the shorter duration – their money is not outstanding for as long. Further, the lender is advantageously positioned to solicit a new loan from the borrower at the 30-year mark. These advantages should translate into a better rate than for the 40-year loan. Few borrowers will or should concern themselves with the prospect of having to refinance after 30 years.

Is a Residual Balance Loan the Same as a Balloon Loan? The astute reader will realize that what I am calling a 30-year residual balance loan is the same as a 30-year balloon loan with a term of 40 years. That is, the payment is calculated over 40 years but the balance must be repaid after 30 years. I have a reason for giving it a different name.

Existing balloon loans have a term of 30 years, with the balance due after five or seven years. They are viewed as close substitutes for adjustable-rate mortgages (ARMs) having initial rate periods of five or seven years. The major difference is that the balloons have no caps on the interest rate change at the end of the period.

A balloon mortgage on which the balance is not due for 30 years, however, is for all practical purposes a fixed-rate mortgage (FRM), since very few borrowers will have the mortgage for 30 years. Because it will appeal to a different type of borrower, and because lenders will price it off other FRMs rather than off ARMs, it deserves a different name.

15-Year Loans With a Residual Balance: The residual balance loan has even more potential as a modification of 15-year than of 30-year loans. 15-year loans carry a significantly lower rate than 30-year loans but most borrowers can’t afford the payment.

For example, a \$100,000 loan for 15 years at 5.375 percent has a payment of \$810.47, compared to \$599.56 on the 30-year at 6 percent. But a 15-year with a residual balance of \$58,173 would have the same payment as the 30, making it affordable to a much larger segment of the market.

From the lender’s perspective, the 15-year with a residual balance has a little more default risk because it amortizes more slowly than the standard 15, and it has a slightly longer duration. These might call for a rate about 1/4 percent higher than on the unmodified 15. But that would still add up to a dynamite product for the borrower.

The writer is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at www.mtgprofessor.com.

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