Rule of 78s: Unearned Interest Calculation Method for Installment Loans

The Rule of 78s is an interest calculation method commonly used for installment loans with add-on interest. This method is most applicable to loans with predefined monthly payments over a stipulated period. It facilitates the computation of unearned interest, especially in cases where the borrower opts for early repayment.

Mechanics of the Rule of 78s

The “78” in the Rule of 78s derives from the sum of the digits from 1 to 12, which represents the number of months in a year (i.e., 1 + 2 + 3 + … + 12 = 78). For different loan terms, the sum changes accordingly.

Key Concept: Unearned Interest

Unearned interest is the portion of the total interest that hasn’t yet been earned by the lender due to early loan repayment.

Example Calculation:

Consider a 12-month loan of $1,000 with an 8% add-on interest rate. The total interest is:

The total payment over 12 months is:

Monthly payment:

Prepayment Scenarios:

• After 1 Month: Unearned Interest: \((12/78) \times 80 = 12.31\)

• After 2 Months: Unearned Interest: \(\frac{12 + 11}{78} \times 80 = 23/78 \times 80 = 23.59\)

• After 11 Months: Unearned Interest: \((1/78) \times 80 = 1.03\)

Considerations

• Legality: Certain jurisdictions have regulations against the Rule of 78s due to its accelerated interest earning, which may not favor the borrower.
• Consumer Impact: Borrowers often pay more interest in the initial months, making early repayment less beneficial.

Applicability in Different Loans

• Installment Loans: Ideal for loans with fixed monthly payments.
• Precomputed Loans: Suitable for loans with interest calculated upfront.

Related Terms

• Add-On Interest: Interest calculated upfront and added to the loan’s principal.
• Amortization: Gradual repayment of a loan through scheduled payments.
• Precomputed Interest: Interest calculated at loan inception and included in the payments.

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