A Not-So-Simple Truth About Interest

By Jack Guttentag
Saturday, January 26, 2008

Q: I am perplexed at what appears to be a nomenclature problem that the mortgage industry has created with its definition of "simple-interest mortgage." Aren't most monthly payment mortgages simple interest?

A: They are, and I agree that the nomenclature can be confusing.

Two concepts are involved. One is a distinction between simple interest and compound interest. The second is a distinction between monthly and daily interest accrual. Borrowers who don't understand these distinctions may not be able to manage their mortgages properly.

Simple interest means that interest is not paid on interest. Compound interest is, or can be, paid on interest.

The distinction can be easily understood in connection with savings instruments. Suppose a bank pays an annual rate of 3 percent, or 0.25 percent a month. On a $100,000 deposit, the account would earn $250 in the first month. If it were a simple-interest account, the bank would also pay $250 in the second month. If it were a compound-interest account, it would pay interest of $250.63 in the second month, the 63 cents being the interest on the $250 earned in the first month.

If the bank paid simple interest, the depositor could withdraw the $100,250 after the first month and place it in another bank that pays interest on the entire amount. This would impose a needless cost on depositors. To my knowledge, there are no simple-interest deposit accounts. Nobody objects to banks paying depositors interest on interest. However, some people object to lenders charging interest on interest.

Mortgages can also be simple interest or compound interest. However, the only compound-interest mortgages are those involving negative amortization, in which the payment does not cover the interest. If unpaid interest is added to the balance, as it is on a negative-amortization loan, interest is calculated on a balance that includes unpaid interest, which makes it a compound-interest loan.

The interest accrual period is the period over which interest is credited. If interest is credited monthly on a savings account, as in my earlier example, the consumer who closes an account before the month is up receives no interest for the month. If interest accrues daily on that account, it would earn $8.22 the first day, with the interest credit rising slightly over the month as each day's interest is added to the previous day's balance.

Mortgages can also accrue interest monthly or daily. With monthly accrual, the quoted annual rate (for example, 6 percent) is divided by 12, and that number is multiplied by the loan balance at the end of the preceding month to get the interest due for the month. With daily accrual, the annual rate is divided by 365, and that number is multiplied by the loan balance at the end of the preceding day to get the interest due for the day.

Given these distinctions, there are two kinds of mortgages in the United States. One accrues interest monthly, and it is simple interest except when it allows negative amortization. This mortgage has no special name because most mortgages are of this type.

The second kind of mortgage accrues interest daily and is always simple interest. This kind ought to be called a daily accrual mortgage to clearly distinguish it from the standard mortgage. But it isn't; it is called a simple-interest mortgage.

I suspect that a major reason for the practice is lender sensitivity to the legal environment. Prohibitions against charging interest on interest have been enacted at various times in some states. By designating their daily accrual loans as simple-interest loans, lenders are advertising that they are not charging interest on interest.

Borrowers can avoid confusion if they understand that a simple-interest mortgage is one that accrues interest daily and should be managed differently from monthly accrual mortgages. With a daily accrual mortgage, every day that borrowers delay their payment results in the accrual of another day of interest. The grace period is not a period free of interest but the period within which they must pay to avoid an additional late charge. The smart borrower with a daily accrual mortgage consistently pays early.

If the mortgage is not simple interest, then it is a monthly accrual mortgage on which the grace period is an interest-free period. The smart borrower consistently pays at the end of the grace period.

Jack Guttentag is professor of finance emeritus at the Wharton School of the University of Pennsylvania. He can be contacted through his Web site, http://www.mtgprofessor.com.

Copyright 2008 Jack Guttentag

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