Rules of thumb are simple methods used to quickly estimate interest-related values without complex calculations. Two commonly known rules are the Rule of 78s and the Rule of 72. These methods were especially useful before computers became widely available and are still helpful for quick understanding.
Rule of 78s (Sum of Digits Method)
Meaning and Background
The Rule of 78s is a method that was used to calculate interest on loans, especially in the United States, before the use of modern computing systems. It is called the “sum of digits” method because, for a 12-month loan, the sum of numbers from 1 to 12 equals 78.
How It Works
In this method, the total interest of the loan is calculated in advance and then distributed across the loan period in a decreasing manner. Although the monthly payments remain the same, the portion of interest in each payment reduces over time.
For example, in a one-year (12-month) loan:
- First month: 12/78 of total interest is charged
- Second month: 11/78
- This pattern continues until
- Twelfth month: only 1/78 of interest is charged
Practical Effect
This method results in a higher portion of interest being paid in the early months of the loan. By the middle of the loan (around 6 months), nearly three-fourths (¾) of the total interest has already been paid.
Because of this:
- Early repayment becomes costly
- Borrowers do not benefit much from paying off the loan early
- The actual cost of borrowing becomes higher than the stated APR (Annual Percentage Rate)
Legal Status
Due to its unfair impact on borrowers:
- In 1992, the United States banned the use of Rule of 78s for:
- Mortgage refinancing
- Consumer loans longer than five years
- Many other countries have also restricted or banned its use, especially for consumer loans
Rule of 72
Meaning and Purpose
The Rule of 72 is a simple formula used to estimate how long it takes for an investment to double when interest is compounded.
Formula
Time (years) = 72 ÷ Interest Rate (%)
This gives an approximate number of years required for money to double.
Examples
- At 6% interest:
72 ÷ 6 = 12 years - At 18% interest:
72 ÷ 18 = 4 years
Actual calculation: 1.18⁴ ≈ 1.9388 (close to doubling) - At 24% interest:
72 ÷ 24 = 3 years
Actual calculation: 1.24³ ≈ 1.9066 (slightly less than double)
Accuracy of the Rule
- Works best for interest rates up to 10%
- Still provides a reasonable estimate for higher rates, though accuracy decreases slightly
Key Differences Between the Two Rules
| Basis | Rule of 78s | Rule of 72 |
|---|---|---|
| Purpose | Loan interest allocation | Investment growth estimation |
| Usage | Loan repayment structure | Time to double money |
| Nature | Complex impact on borrowers | Simple and practical |
| Status | Restricted in many countries | Widely used |
Conclusion
Both rules simplify financial calculations but serve very different purposes. The Rule of 78s was mainly used in loan interest distribution but is now restricted due to its unfair impact. On the other hand, the Rule of 72 remains a popular and useful tool for quickly estimating investment growth and understanding the power of compound interest.