Rule of 78 Explained: Usage by Lenders and Calculation Method
Explore the Rule of 78, learn how lenders use this method, and understand the calculation process involved.
The Rule of 78 is a method of calculating how much precalculated interest a lender refunds to a borrower who pays off a loan early. It is also known as the sum-of-the-digits method.
Usage by Lenders
Lenders use the Rule of 78 to calculate the amount of interest that a borrower must pay over the life of a loan. This information is then used to calculate the borrower's monthly payments.
The Rule of 78 is beneficial for lenders because it ensures that they receive a certain amount of interest, even if the borrower pays off the loan early. This is because the Rule of 78 weights the interest payments towards the beginning of the loan term.
Calculation Method
To calculate the amount of interest that must be refunded to a borrower who pays off a loan early using the Rule of 78, follow these steps:
- Sum the digits of the loan term. For example, for a 12-month loan, the sum would be 1 + 2 + 3 + ... + 12 = 78.
- Divide the number of months remaining on the loan term by the sum of the digits. For example, if a borrower with a 12-month loan pays off the loan after 6 months, the fraction would be 6 / 78.
- Multiply the fraction by the total amount of interest that was charged on the loan. This will give you the amount of interest that must be refunded to the borrower.
Example
A borrower takes out a 12-month loan for $10,000 at an interest rate of 5%. The total amount of interest charged on the loan is $500.
The borrower makes all of their payments on time, but they decide to pay off the loan early after 6 months. To calculate the amount of interest that must be refunded to the borrower, we follow the steps above:
- Sum the digits of the loan term: 1 + 2 + 3 + ... + 12 = 78
- Divide the number of months remaining on the loan term by the sum of the digits: 6 / 78 = 1/13
- Multiply the fraction by the total amount of interest that was charged on the loan: 1/13 * $500 = $38.46
Therefore, the lender must refund $38.46 of interest to the borrower.
Conclusion
The Rule of 78 is a method of calculating how much precalculated interest a lender refunds to a borrower who pays off a loan early. It is a beneficial method for lenders because it ensures that they receive a certain amount of interest, even if the borrower pays off the loan early.
Rule of 78: Definition, How Lenders Use It, and Calculation.
The Rule of 78, also known as the Sum of Digits method, is a technique used in some financial and lending contexts to calculate interest charges or refunds on a loan. It's named the "Rule of 78" because the sum of the digits 1 through 12 (for a 12-month loan) equals 78. This method is less commonly used today and is often considered outdated, as it can be less favorable for borrowers in certain situations. It's crucial to understand how it works, how lenders use it, and how to calculate it:
How it works:
Allocation of Interest: The Rule of 78 allocates a higher portion of the total interest cost to the earlier months of a loan, and a smaller portion to the later months.
Front-Loading Interest: This means that the majority of the interest charges are paid in the initial months of the loan. Therefore, if a borrower decides to pay off the loan early, they may end up paying a substantial amount of interest, even if the loan term is not completed.
How lenders use it:
Lenders use the Rule of 78 to calculate how much interest a borrower owes if they decide to prepay or settle the loan before its scheduled maturity date. This method can make it more costly for borrowers to pay off their loans early, as a significant portion of the interest has already been front-loaded, and they may not receive much interest refund.
Calculation:
To calculate the interest charges or refunds using the Rule of 78, follow these steps:
Determine the loan term: First, establish the original term of the loan, which is often expressed in months.
Calculate the sum of digits: Find the sum of the digits for the loan term. For a 12-month loan, the sum would be 78 (1 + 2 + 3 + ... + 12).
Calculate the interest for each month: Allocate the total interest to each month by dividing the sum of digits for that month's digit by the total sum of digits. For example, for a 12-month loan:
- For the first month, it would be: 12 / 78 * Total Interest
- For the second month, it would be: 11 / 78 * Total Interest
- For the third month, it would be: 10 / 78 * Total Interest
- And so on...
Interest refund (if prepaying): If the borrower decides to prepay the loan before its full term, the lender calculates the unearned interest by summing the interest for the remaining months (e.g., months 4 through 12).
The Rule of 78 can make early loan payoff more expensive for borrowers compared to other methods like the simple interest method, which allocates interest evenly over the life of the loan. Because of this, it's important for borrowers to be aware of the calculation method used in their loan agreements and understand the potential costs of early repayment. In many cases, the Rule of 78 has been replaced by more borrower-friendly methods and may not be used in modern lending practices.