A Prepayment Penalty: the Rule of 78s

ave you ever wondered how much of your car payment each month goes to the financing cost and how much of it goes to paying off the loan? The rule of 78s is one method some lenders use to calculate how much interest you pay each month on installment loans.

The rule of 78s,
also called the
sum of digits method,
gets its name
because the sum
of digits 1 through 12,
the months in a
one-year loan,
is 78.

Rule of 78s vs. simple interest
When lenders use the rule of 78s, they distribute the total finance charge over all payments but charge more interest early in the loan term and less later, compared with other methods. "The rule of 78s, also called the sum of digits method, gets its name because the sum of digits 1 through 12, the months in a one-year loan, is 78," explains Steve Rick, senior economist at CUNA & Affiliates in Madison, Wis.

Here's how the rule of 78s works for a 12-month loan: You pay 12/78 of the total finance charge the first month, 11/78 the second month, 10/78 the third month, and so on. The rule of 78s applies the same way for long-term loans. For example, a 24-month loan—where the sum of the digits for months one through 24 is 300—would have a first month's interest of 24/300, second month's interest of 23/300, and 22/300 for the third month. Interest on a 36-month loan would be broken into 666 parts.

In contrast, credit unions traditionally charge simple interest on a declining balance, which calculates the interest according to the formula:

interest due =	annual percentage rate (APR)
	No. of payments x balance

This method assesses interest only for the period that you use the money. With both loan calculation methods, each monthly payment is part principal and part interest; the rule of 78s assigns more interest to early payments than does the simple interest approach.

Why should you care? It can cost you if you're thinking about paying off—or refinancing—a rule of 78s loan before it matures. "The rule of 78s is a method for refunding unearned interest when an installment loan is paid off before maturity," Rick says.

Rick says lenders frequently use the rule of 78s for personal loans and auto loans because it's "very quick and simple to apply to a prepaid loan." For example, if you took out a four-year, $18,000 car loan with a 9% APR and decided to prepay your loan entirely in the 12th month of the loan period, your prepayment interest refund—calculated using simple interest—would be $2,039.52. The rule of 78s prepayment interest refund would be $1,982.53, a difference of $57. (See chart.)

The chart shows the cost to the borrower when a lender uses the rule of 78s method to calculate the unearned interest refund, relative to the simple interest method on a four-year, $18,000 auto loan with a 9% APR. If the borrower prepays the loan after 16 months, he or she would receive about $60 less in interest refund compared with an institution using the simple interest method. The interest refund loss increases up to 16 months because the rule of 78s allocates more of each monthly payment as interest than does the simple interest method.

The rule of 78s is only a problem for someone who decides to pay off a loan before the agreed upon term of the loan. "In the end," Rick says, "if the loan is not prepaid and held for the full term, there is no loss to the borrower whether the loan is set up for the rule of 78s or simple interest." He says, "The borrower gets snagged with the rule of 78s because it accelerates the interest recognition by assuming you will pay the total contracted interest, which favors the lender if you prepay. Therefore, it's a hidden prepayment penalty."

Not sure if your loan uses the rule of 78s? Look at your Truth in Lending disclosure. If you see a phrase like "you will not be entitled to any rebate of part of the finance charge if you prepay," ask the lender if it computes interest using the rule of 78s.

     Credit unions
     traditionally
     charge
     simple interest
     on a
     declining balance.
     This method
     assesses interest
     only for the time
     that you use
     the money.