My maths secrets
It’s time to give away one of my on air TV maths secrets. It enables me to look like I’m doing whizz hot calculations in my head eg. when someone says “my debts are at 12%” I can instantly say “at that rate what you’ll owe will double just over every six years”…
The trick…
If you divide 76 by the percentage increase, that tells you roughly the number of years it takes to double. So that’s all I’m doing in my head, it’s not really a quick compounding. I can’t quite remember who told me it, but it was certainly a long time before I became the Money Saving Expert.
Yet it isn’t perfect…
It is only a rough estimate but it has a couple of issues you need to be aware of:
- Problem number 1 – it only works on debts you’re not repaying
While it’s fine for savings (unless you’re adding each month), for debts it only works if you assume that none of the debt is actually being repaid during that time.This is of course rare, with loans and credit cards you’re usually repaying, so it only works with a static overdraft or something like equity release.
Yet it’s still a good indicator and if you then incorporate my trick from a past blog on how to work out personal loan interest in your head you can actually get to a relatively decent estimation.
- Problem number 2 – it’s less accurate for smaller percentages
I’ve always found it slightly more accurate for higher 10% ish type percentages. For lower amounts it varies somewhat and I’ve found using roughly 70 works better for that.
In fact as I’m writing this I’ve just decided to get especially nerdy. I’ve never actually calculated the accuracy of this rule before and I’m going to do just that now. If nothing else that’ll prove I am a genuine nerd, even though I use a short cut trick.
……. time passes …..
OK it’s taken me about 15 minutes on a spread sheet, and I’ll be honest, I’ve had a lot of fun doing it. I do get a kick out of doing silly abstract sums sometimes.
I’ve knocked up the table below to test my issue (in fact much of the time was copying and pasting the spread sheets data into a form I could put in the blog).
Rule of 76 |
Rule of 73 |
Rule of 70 |
||||
Percentage Interest |
Years to double |
Actual growth |
Years to double |
Actual growth |
Years to double |
Actual growth |
1% |
76 |
2.13 |
73 |
2.06 |
70 |
2.01 |
3% |
25 |
2.11 |
24 |
2.05 |
23 |
1.99 |
5% |
15 |
2.10 |
15 |
2.03 |
14 |
1.98 |
10% |
7.6 |
2.06 |
7.3 |
2.01 |
7 |
1.95 |
15% |
5.1 |
2.03 |
4.9 |
1.97 |
4.7 |
1.92 |
20% |
3.8 |
1.99 |
3.7 |
1.95 |
3.5 |
1.89 |
30% |
2.5 |
1.94 |
2.4 |
1.89 |
2.3 |
1.84 |
50% |
1.5 |
1.85 |
1.5 |
1.81 |
1.4 |
1.76 |
Key to the table
Just to explain what the figures mean:
Years to double: How long that specific rule predicts it’d take to double
Actual growth: This shows what really happens over the time the rule predicts
The nearer the actual growth is to the number 2, the more accurate the rule is. Thus from the chart…
The rule of 76 is best for percentages between 15% and 30%
The rule of 73 is good for percentages from 5% to 15%
The rule of 70 is best for percentages from 1% to 5%
In other words the higher the percentages the nearer to 80 the rule should be, the lower the nearer to 70.
I enjoyed writing this one, probably much more than anyone reading!
Comment and Discuss
PS. In the forum, discussion to this blog someone has suggested the ‘rule of 76’ is a sub-prime lending rule and the ‘rule of 70’ normal loans. I think that works well – great analogy.
