Rule of 78s

The Rule of 78s is a method for computing unearned interest used on installment loans with add-on interest. It distributes the interest charges in a way that results in higher interest expenses earlier in the loan term.
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Definition and Overview

The Rule of 78s, also known as the “Sum of the Digits” method, is a way to allocate the interest over the term of a loan so that more interest is paid earlier in the loan term. This method is most commonly applied to short-term installment loans.

Detailed Explanation

The name “Rule of 78s” comes from the sum of the digits of the first twelve numbers (1 + 2 + 3 + … + 12 = 78). The Rule of 78s is used to calculate how much interest is “earned” by the lender at any point in time if the borrower decides to pay off the loan early.

Here’s how it works:

  1. Calculation Method: If a 12-month loan is made for $1,000 with an 8% add-on interest, the total interest is $80 (i.e., $1,000 * 0.08). Adding this interest to the loan amount, the total to be repaid is $1,080.

  2. Monthly Payments: The total repayment amount divided by the number of months gives the monthly payment: $1,080 / 12 = $90 per month.

  3. Interest Allocation: At the end of each month, the fraction of the interest considered ’earned’ by the lender is based on the sum of the remaining months’ digits. For instance, if the borrower decides to prepay after 1 month, 12/78 of the interest is considered earned. By the end of the second month, (12 + 11)/78 of the interest is considered earned.

Examples

  • Example 1: A borrower prepays the loan at the end of one month. The earned interest is 12/78 of the total $80 interest, which equals approximately $12.31. The remaining interest ($80 - $12.31) is refunded.

  • Example 2: If the borrower prepays at the end of the second month, the earned interest is (12 + 11)/78 of the $80 interest, which equals approximately $23.59. The remaining interest ($80 - $23.59) is refunded.

Frequently Asked Questions (FAQs)

Q1: Why is the Rule of 78s considered unfavorable for borrowers?

  • A1: The Rule of 78s front-loads the interest payments, meaning borrowers pay a higher portion of the interest in the early months of the loan. This can make early repayment less financially beneficial.

Q2: Is the Rule of 78s still used for modern loans?

  • A2: While the Rule of 78s is less common now due to fair lending laws and consumer protections, it may still be applied in some short-term installment loans. However, many jurisdictions have regulations limiting its use.

Q3: How does the Rule of 78s compare to the actuarial method?

  • A3: Unlike the Rule of 78s, the actuarial method calculates interest based on the outstanding principal balance, resulting in more equitable interest distribution over the loan term.
  • Add-On Interest: A method of calculating interest by adding the total interest to the loan principal upfront, which is then divided into equal installment payments.
  • Actuarial Method: A method of interest calculation where interest is based on the remaining loan balance at each payment interval.

Online References

Suggested Books for Further Studies

  1. “Personal Finance For Dummies” by Eric Tyson
  2. “Principles of Banking” by American Bankers Association
  3. “Fundamentals of Financial Management” by Eugene Brigham and Joel Houston
  4. “Finance and Financial Markets” by Keith Pilbeam

Fundamentals of the Rule of 78s: Finance Basics Quiz

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Thank you for delving into the Rule of 78s with us. We hope this comprehensive guide and quiz has enhanced your understanding of this interest computation method in finance!

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