The big ideaSeventy-two divided by the yearly rate is a quick guess at the years to double.
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.
A bigger rate means fewer years to double.Two ways to find the years.
Example 1: Twelve percent
A garden pays 12 percent.
Divide 72 by the rate: 72 ÷ 12 = 6.
It takes about 6 years to double.
Example 2: 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.
Example 3: 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.
Example 4: 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.
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
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?
To double in 12 years, what rate does a garden need?
Is the rule of 72 exact?
A garden pays 6 percent. About how many years to double?
Answers: 1. 4 years · 2. 6 percent · 3. No, it is a close guess · 4. 12 years
Try at homeWith 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.
For grown-upsTry 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.
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