What Is the Rule of 78?

The Rule of 78 Explained in Less Than 5 Minutes

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The Rule of 78 is a mathematical method that some lenders use to calculate how much a borrower has already paid toward any interest, credit insurance, or finance charges during the life of a loan. The Rule of 78 can come into play when a borrower wants to repay their loan before it reaches maturity, when they may qualify for a refund of some of these charges.

Learn more about how the Rule of 78 works and how lenders use it. 

Definition and Examples of the Rule of 78

If you’re considering paying off a loan early, it can be helpful to know how much you’ll save on interest by repaying the loan before it matures. While it may seem like it’s always a good idea to repay a loan as quickly as possible, in some cases you can profit more by investing your money than you would save on interest payments. The Rule of 78 can be used to help determine how much of a refund you’ll get for any interest payments, finance charges, or credit insurance premiums once you repay your account in full.

The Rule of 78 structures interest and payments such that borrowers pay more interest at the beginning of a loan and pay less in interest as they pay down their debt.  If you are far along in the debt repayment process, the Rule of 78 may reveal that paying off your loan early won’t save you that much money. 

Some lenders use the Rule of 78, also known as "the sum of the digits," to figure out just how much interest a borrower has already paid on a loan. Because of the Truth in Lending Act, lenders have to disclose to borrowers if they are entitled to a refund when they pay off their loan early. Even so, if you’re planning on repaying a loan early, don’t wait for your lender to bring up any potential refunds. It’s always worth inquiring about a refund on your own.  

The reason that the Rule of 78 is also known as the sum of the digits, is because 78 is a sum of the digits of the months in a year: 1 + 2 +3 + 4 +5 + 6 + 7 + 8 + 9 + 10 + 11 +12 = 78. 

In accordance with the Rule of 78, every month in a borrower’s contract is assigned a value. This value is exactly the reverse of its occurrence in the contract. For example, month one of a 12-month contract is assigned the value 12. Month two is assigned the value 11 and so on. By the end, month 12 has a value of 1. As each month elapses, the lender earns interest that is equal to the total value of the expired months.

Let’s look at an example of how this can work. 

Let’s say you prepay a loan after two months of a 12-month contract. Doing so would allow the lender to keep 29.49% of the finance charges (first month (value of 12) + second month (value of 11) = 23/78 or 29.49%). 

How the Rule of 78 Works

The Rule of 78 provides a method for calculating refunds of interest for any precomputed consumer credit transaction. It can be simpler to calculate than other methods and is more favorable to lenders than borrowers. Since Sept. 30, 1993, in order to qualify for the Rule of 78, the loan term must exceed 61 months. Some states prohibit the use of the Rule of 78 altogether.

This formula illustrates how to compute a refund using the Rule of 78: 

(U x (U + 1)) \ (T x (T + 1)) = Rule of 78 refund fraction x F = Refund

  • U: Unearned term periods
  • T: Term periods 
  • F: Finance charge

Let’s look at this formula in action, with a 12-month contract that the borrower prepaid at three months (leaving nine months unearned). They have a finance charge of $100.

  • U = 9
  • T = 12
  • F = $100

(9 x (9 + 1)) \ (12 (12 + 1)) = (9 x 10) \ (12 x 13) = 90 \ 156 = 0.5769 

0.5769 x $100 (finance charge) = $57.69 refund 

Alternatives to the Rule of 78

The Rule of 78 is not the only method for computing interest (and refunds of precomputed unearned interest if a loan is repaid early). Other methods are Simple Interest, Actuarial, and Daily Simple Interest.  

Key Takeaways

  • The Rule of 78 is used to calculate a borrower’s interest refund for paying back a credit product early.
  • The Rule of 78 is also known as "the sum of the digits” because of the way it assigns value to months of the year.
  • The Truth in Lending Act mandates that lenders disclose to borrowers if they are entitled to a rebate after paying off a loan early.