This blog looks at some old, even odd, number rules. We live with them all the time and often refer to them.

The 80:20 rule
The other day I was reading the Bizezia publication: Glossary of Marketing Terms and, for some unknown reason, arrived at the definition of the Pareto Principle: The 80:20 rule: 80% of an outcome will come from 20% of effort.

Wikipedia describes the Pareto Principle in more detail:

  • The Pareto principle (also known as the 80:20 rule, the law of the vital few, and the principle of factor scarcity) states that, for many events, roughly 80% of the effects come from 20% of the causes. Business-management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed in 1906 that 80% of the land in Italy was owned by 20% of the population. Pareto developed the principle by observing that 20% of the pea pods in his garden contained 80% of the peas.

Wikipedia goes on to say that it is a common rule of thumb in business; e.g., “80% of your sales come from 20% of your clients”.

But F. John Reh writing here puts it differently. He says: “The value of the Pareto Principle for a manager is that it reminds you to focus on the 20 percent that matters. Of the things you do during your day, only 20 percent really matter. Those 20 percent produce 80 percent of your results. Identify and focus on those things. When the fire drills of the day begin to sap your time, remind yourself of the 20 percent you need to focus on. If something in the schedule has to slip, if something isn’t going to get done, make sure it’s not part of that 20 percent.”

His article concludes:  Apply the Pareto Principle to all you do, but use it wisely.

There’s a good article by Kalid Azad, here.

Do you believe in the Pareto Principle and if you do, how has it helped you in your business or private life. Please email me at or comment below.

The Rule of 72
Then, I came across another mathematical rule this week. It’s called “The Rule of 72”. It enables you to estimate the effect of any growth rate if you want to double your money. The formula is: Years to double = 72/Interest Rate.

You can use this formula for any financial estimate using compound interest. Some examples are:

  • At 6% interest, the millions you have in savings takes 72/6 or 12 years to double.
  • Since nobody I know gets 6% on their money, let’s take 0.5% which is what most banks pay. At that rate, your money takes 72/0.5 or 144 years to double.
  • To double your money in 10 years, you will need an interest rate of 72/10 or 7.2%.
  • If your country’s GDP grows at 3% a year, the economy doubles in 72/3 or 24 years.  3% isn’t on the horizon for the UK, the estimated annual growth rate has now risen from 1.5% to 1.9% (see here) so it will take 72/1.9 or nearly 38 years to double.

The Rule of 37037
Have you heard of the rule of 37,037?  It’s quite simple really although I haven’t worked out why it works. Just multiply 37,037 by any single number (1-9), then multiply that number by 3. Every digit in the answer will be the same as that first single number. Try it. Then perhaps you can explain to me why it works and what can be done with this invaluable information.

The Rule of 78
As every accountant knows (or should know) the Rule of 78 is also known as the sum-of-the-digits method used in lending that refers to a method of yearly interest calculation.

If you take the digits, 1 to 12 and add them up, you get a total of 78. The name of the rule comes from the total number of months’ interest that is being calculated in a year (the first month is 1 month’s interest, whereas the second month contains 2 months’ interest, etc.).

When I was a student accountant, I was told about this rule since finance companies and banks used it to calculate the interest spread over the loan period. So, if the loan was for a 12 month period, the interest accrued 12/78 ths in the first month, 11/78 ths in the second month and so on until the 12th month at which time 1/78th of the interest is that month’s portion of the total interest charge.

I was taught to apportion the interest cost to include in accounts using this method. The method was used by lenders to calculate how much interest to charge for loans paid off early. For example, if a 12-month loan is paid off at month 11, the lender will want 77/78ths (of the total interest to settle and allows only 1/78th rebate for early settlement.

The formula to arrive at the sum of the digits for any loan for any period is found by taking N/2 x (N+1) – where N is the number of months in the loan period.  So for a 24 month period, the sum of all the digits from 1 to 24 is (12*25) = 300.

I recall that the formula was used a lot with hire purchase agreements, particularly for the purchase of cars.

Martin Pollins
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