What Is the Rule of 78s and How It Affects Your Loan
Explore the Rule of 78s, a historical loan interest allocation method that front-loads costs. Understand its past and diminishing modern relevance.
The Rule of 78s is a method historically used by lenders to calculate and allocate interest on precomputed installment loans. Its primary function is to front-load a larger proportion of the total interest into the initial payments. This method was relevant for loans where the finance charge was determined upfront and added to the principal balance, influencing how interest is considered paid throughout the loan term.
Understanding the Rule of 78s
The Rule of 78s, also known as the “sum of the digits” method, is an interest allocation technique that assigns a share of a loan’s total interest to its early payment periods. This method derives its name from a 12-month loan: the sum of the digits from 1 to 12 (1+2+3+…+12) equals 78.
Historically, this method gained traction because of its simplicity in manual calculations before computer use. The underlying principle is that a borrower has the use of a portion of the loan principal at the beginning of the loan term, justifying higher interest charges during those initial periods.
This approach pre-calculates the total interest for the entire loan term and then distributes it unevenly across the repayment schedule.
Calculating Interest with the Rule of 78s
Calculating interest using the Rule of 78s involves a formula that distributes the total finance charge over the loan’s term. The total interest is determined at the outset and divided into portions based on fractions.
To calculate the denominator, sum the integers for each payment period. For instance, a 12-month loan uses a denominator of 78 (1+2+…+12). For longer loans, the sum of the digits for the total number of months in the loan term is used. For example, a 24-month loan would use a denominator of 300. For a loan with ‘N’ months, the sum of the digits can be calculated using the formula N (N + 1) / 2. For example, a 36-month loan would have a denominator of 666.
The numerator for each period is the number of remaining payment periods, counting backward from the original loan term. For a 12-month loan, the first month uses 12 as the numerator, the second uses 11, and so on, until the last month uses 1. Each month’s allocated interest is calculated by multiplying the total finance charge by a fraction: (remaining months / sum of digits).
For example, consider a 12-month loan with a total precomputed interest of $780. In the first month, the interest allocated would be (12/78) $780 = $120. In the second month, it would be (11/78) $780 = $110. This continues until the last month, which has (1/78) $780 = $10 allocated as interest.
Implications for Borrowers
The Rule of 78s impacts borrowers, especially those who pay off loans ahead of schedule. A disproportionately large amount of the total interest is paid during the early part of the loan term, meaning early payments still largely go toward satisfying the pre-allocated interest.
If a borrower repays a loan calculated using the Rule of 78s before its full term, interest savings are less than what they would be with a simple interest loan. Under simple interest, interest is calculated on the declining principal balance, allowing for interest savings with early repayment.
Consequently, a borrower who pays off a loan in half the time might find they have already paid over half of the total interest originally calculated. This makes the Rule of 78s unfavorable for borrowers who aim to reduce their interest costs by accelerating their loan payments.
Modern Application and Legal Status
The use of the Rule of 78s has declined, particularly for consumer loans, due to increased consumer protection regulations and the availability of computing power. Modern technology allows for calculation of simple interest, which is more transparent and beneficial for borrowers. Despite its diminished use, it might still be encountered in contexts, such as older loan agreements or types of commercial credit.
Federal law has restricted the application of the Rule of 78s for consumer credit transactions. Under the Truth in Lending Act (TILA), this method is prohibited for loans with maturities exceeding 61 months that were consummated after September 30, 1993.
Beyond federal restrictions, states have also implemented their own prohibitions or limitations on the Rule of 78s for consumer loans, regardless of the loan term. Some states have banned it entirely for all consumer credit, while others may limit its use to loan types or amounts. Lenders are often required to provide disclosure if this method is used.