How it works
A garden's rate says how many coins it adds for every hundred. Six new coins for every hundred is a rate of six percent.
The shortcut: divide 72 by the rate to guess how many years a garden takes to double. No counting year by year.
It is a close guess, not exact. A good guess with a little error is called an approximation.
72 splits evenly many ways (2, 3, 4, 6, 8, 9 or 12), which makes it easy to divide in your head.
Worked examples
Twelve percent
- A garden pays 12 percent.
- Divide 72 by the rate: 72 ÷ 12 = 6.
- It takes about 6 years to double.
Nine percent
- A garden pays 9 percent.
- 72 ÷ 9 = 8.
- It takes about 8 years to double. The 9 is the rate, not the years.
Working backwards
- Nico wants to double in 9 years.
- Divide 72 by the years: 72 ÷ 9 = 8.
- A garden paying 8 percent doubles in about 9 years.
Where it drifts
- At 36 percent the rule says 72 ÷ 36 = 2 years.
- But after 2 years the garden holds only 185, not 200.
- 200 − 185 = 15, so the shortcut is rougher far from the middle.
A taste of the worksheets
These are some of the questions on the sets. The printable sheets have more and an answer key.
- Working backwards: to double in 9 years, divide 72 by 9. The rate is ___ percent.
- True or false? Mo says: the rule of 72 is exact every single time. Is Mo right?
- Tia says: at 9 percent a garden takes 9 years to double, because the rate is 9. What did Tia mix up? She should have multiplied 72 by 9 / She should have used the rate as 90 / She used the rate as the years: 72 ÷ 9 = 8
- Circle every true sentence about the rule of 72. It gives a close guess at the years to double / It is exact every time / It works backwards too / It promises what a real garden will do / 72 splits evenly many ways, so it is easy to divide
- At 36 percent the rule says 2 years, but the garden holds only 185. That is ___ coins short of 200.
Words to know
- rate
- How many coins a garden adds for every hundred.
- percent
- How many for every hundred: six percent is six for every hundred.
- double
- Grow to twice as much.
- approximation
- A good guess with a little error.
Watch out for
- The answer is years, not coins and not a percent.
- Divide 72 by the rate. Do not use the rate as the years: 72 ÷ 9 is 8, not 9.
- It is a close guess, not exact, and it drifts at very high rates.
- These rates are made up. Real ones change and nothing is promised.
Try it
About how many years does a garden paying 18 percent take to double?
4 years. 72 ÷ 18 = 4.
To double in 12 years, what rate does a garden need?
6 percent. 72 ÷ 12 = 6, working backwards.
Is the rule of 72 exact?
No, it is a close guess. It is an approximation, a good guess with a little error.
A garden pays 6 percent. About how many years to double?
12 years. 72 ÷ 6 = 12.
For grown-ups
With a grown-up, divide seventy-two by four different rates. Then use a calculator to double a hundred again and again, and see how close the rule gets.
Try the rule on four different rates together, then use a calculator to double 100 again and again and see how close the rule gets. The rates are made up: this is a thinking tool, not a promise or advice about any real money.