# Investigating the Rule of 70

Interest:% (annual)

For every interest rate there is a doubling time: the time it takes to double the initial amount. For instance, if you invest £1000, how long will it take to get to £2000?

A rough-and-ready way to get the doubling time is to divide 70 by the interest rate. For example, with an interest rate of 3%, divide 70 by 3 to get 23⅓ years, which is very nearly correct.

Move the slider to change the interest rate, or just type in a new rate. The doubling time and its approximation appear below.

#### If a Bank cuts its interest rate from 1.5% to 1.25%, how much has it extended the doubling time?

Just under a decade (from 46 and a half years to nearly 56 years)

#### When is the rule of 70 most accurate?

When the interest rate is 2%, the rule gives a doubling time of 35 years, which is right to two decimal places.

#### When does the rule give too small a value?

When the rate is less than 2%.

#### What is the percentage error when the interest rate is 40%?

The correct number is 2.06. The rule of 70 gives 1.75 years, so the error is 0.31.

As a percentage, this is (0.31 / 2.06) x 100, which equals 15. So the Rule of 70 is 15% out from the correct value.

Doubling time: yrs
Rule of 70     : yrs