# What is the Rules of 78s?

John Lister

The rules of 78s is a method used to calculate interest. It means that the interest payments decrease disproportionately during the course of the loan period. Although the method appears fair at first glance, it favors the lender and means the borrower will be penalized for early repayment.

With many loans, interest is applied on a simple basis. Whenever interest is added, it is simply calculated as a proportion of the outstanding balance. The simplest example of this would be if a borrower took out a loan at 10% interest charged annually. If, at the end of the first year, they still owed \$100 United States Dollars, \$10 would be added in interest. Another variation of the system works by calculating interest monthly, with a fixed rate applied each month.

With the rules of 78s, a different rate is applied each month. The annual interest is calculated and then arranged monthly so that more is collected in the earlier months and less in the later months. The name comes from the fact that 1 plus 2 plus 3, and so on up to 12, equals 78.

To calculate the monthly loan payments, the annual interest charge is divided by 78. In the first month of the year, the borrower pays 12/78ths of the year's interest. In the second month of the year, the borrower pays 11/78ths of the interest. This continues until the 12th month of the year when they pay just 1/78th of the interest.

Although the rules of 78s system only literally applies to a one-year loan with monthly repayments, the principle can be used for any loan period. The only difference is that the numbers are adjusted to meet the circumstances. For example, with a 24-month loan, the total of the numbers 1 through 24 is 300. The borrower would thus pay 24/300ths in the first month, 23/300ths in the second month and so on.

While unusual, the rules of 78s process makes no practical difference to somebody who pays the loan off across the agreed timescale. This is because they wind up paying the same amount of interest. Where the rules of 78s really are noticeable is when the lender wants to pay off the loan early. This is because they will have already paid a disproportionate share of the total interest, which will not be refunded.

To put this into context, a borrower paying off the balance of a loan six months into a 12-month agreement that uses the rules of 78s will have paid around 75% of the interest. The front-loading of interest is so extreme that the borrower will actually pay almost a third of the annual interest in their first monthly payment.

To make things even worse, many lenders simply collect a fixed amount each month, from which they take the interest payment and then only apply the remaining amount towards reducing the balance. This means that the majority of the money the borrower pays in the early months goes to interest rather than repaying the loan. This makes early repayment even more costly as, for example, halfway through the loan period the borrower will have paid half the money they were scheduled to pay for the entire loan period, but the outstanding balance will be considerably more than half the loan amount.