Before calculators, spreadsheets and AI, accountants had a few tricks of their own
Opening
I recently asked AI to help me remember a very simple bit of mathematics my father used to use when estimating the interest on a long-term loan.
That got me thinking about how different accounting was when I started out.
There were quite a number of little rules and shortcuts that the older accountants seemed to carry around in their heads. They could do surprisingly complicated calculations without a calculator, spreadsheet or, for that matter, Google.
They weren’t always looking for an answer accurate to the last cent. They were looking for an answer that was good enough to make a decision – and they could usually get there remarkably quickly.
And occasionally, they were useful for impressing a client.
The old accountant’s estimate
The method my father used was remarkably simple.
Suppose you wanted to estimate the interest on a loan where the principal was being repaid over a number of years.
Instead of reaching for a calculator and calculating the interest month by month, you could make a rough assumption that, on average, half of the original capital would be outstanding during the term of the loan.
For example:
R4 million at 10% for 5 years
Simple interest on the full R4 million would be:
R4 million × 10% × 5 years = R2 million
But because the loan balance would gradually decline as capital was repaid, the average amount outstanding would be approximately half the original loan.
So:
R2 million ÷ 2 = approximately R1 million interest
It isn’t an exact calculation. But it gives you a remarkably useful back-of-the-envelope answer.
And, more importantly, it could be calculated in your head.
That was often all you needed to decide whether a proposed transaction was worth investigating further.
The Rule of 72 – the accountant’s party trick
One of the most famous financial shortcuts is the Rule of 72.
It answers a simple question:
How long will it take my money to double?
Divide 72 by the annual interest or investment return.
At 6%:
72 ÷ 6 = 12 years
At 8%:
72 ÷ 8 = 9 years
At 12%:
72 ÷ 12 = 6 years
It isn’t exact, but it is remarkably useful for mental calculations.
And it works in reverse too.
If someone tells you they expect their investment to double in 10 years, you can immediately estimate the required return:
72 ÷ 10 ≈ 7.2%
No calculator required.
The Rule of 70 – what inflation is doing to your money
The Rule of 70 is another useful shortcut.
Divide 70 by the inflation rate to estimate how long it will take for the purchasing power of money to halve.
At 5% inflation:
70 ÷ 5 = 14 years
At 7% inflation:
70 ÷ 7 = 10 years
That doesn’t mean the number in your bank account has fallen by half.
It means that, after roughly ten years of 7% inflation, you would need about twice as much money to buy what the original amount could buy today.
That is a useful distinction – particularly when discussing long-term savings and retirement planning.
The Rule of 115 – from doubling to tripling
If the Rule of 72 tells you approximately how long it takes to double your money, the Rule of 115 gives you a quick estimate of how long it takes to triple it.
Divide 115 by the annual rate of return.
At 10%:
115 ÷ 10 = 11.5 years
So an investment earning 10% a year would take approximately 11½ years to triple.
Again, it is an approximation rather than a substitute for proper financial modelling.
But that’s exactly the point.
These rules were never intended to replace proper calculations.
They were intended to get you into the right ballpark very quickly.
The Rule of 78 – the slightly odd one
Then there is the Rule of 78, which is quite different from the others.
It was a method historically used to calculate how interest was allocated over the life of certain installment loans when a borrower paid the loan off early.
The name comes from the sum of the numbers 1 to 12:
1 + 2 + 3 + … + 12 = 78
Under the method, the interest was weighted towards the earlier months of a one-year loan. Month one was allocated 12/78 of the total interest, month two 11/78, and so on, down to 1/78 in the final month.
In other words, it was a way of front-loading the interest.
It is not something I would recommend using for modern financial calculations – and there are regulatory restrictions on its use in some jurisdictions – but it is an interesting example of the sort of numerical shortcut that was once part of the financial world.
Why did these tricks matter?
Today, I can type a question into AI and have the answer in seconds.
A spreadsheet can calculate hundreds of repayment scenarios.
A financial calculator can produce an amortisation schedule to several decimal places.
And that’s wonderful – except that in the real world, nothing is quite that simple.
The facts on which you build a model are often incomplete, uncertain or subject to unexpected changes. So even the most sophisticated model, built with the best available information, is very seldom going to be 100% right.
More often, a model will show us a range of possible outcomes rather than one definitive answer.
That is where having a few mental shortcuts can still be surprisingly useful.
If you have a good feel for the numbers, you can quickly sense-check the result your model is producing. If the spreadsheet tells you something that seems wildly different from your back-of-the-envelope calculation, that’s a good reason to stop and ask why.
The mental calculation doesn’t replace the model.
It helps you challenge the model.
And there was something rather satisfying about being able to look at a set of figures and say:
“That’s going to cost you roughly a million rand in interest.”
And then, when the client asked, “How do you know that?”, you could explain it on the back of an envelope.
Perhaps that is one thing the old accountants got right.
They didn’t necessarily need to calculate everything to six decimal places.
They needed to understand whether the answer made sense.
A final thought
Perhaps the old geezers weren’t doing mathematics the hard way.
Perhaps they had simply learned which mathematics mattered.
And that, in itself, wasn’t such a bad accounting skill to have.
**#Accounting #Accountants #FinancialTips #MentalMath #Finance #TaxAndAccounting #BusinessTips #OldSchoolAccounting**