How many years does it take before your investment doubles in value?  If we assume the investment is compounding continuously, then we can start with the following formula:

A = Pe^rt

where A is the accumulated value, P is principal, r is the annual interest rate and t is time in years.  A doubling of the principal means that A = 2P and the formula would become:

2P = Pe^rt

  2 = e^rt  , ln 2 = rt, t = ln 2 / r

If we multiply the top and bottom by 100, the previous equation can be re-written as:

t = 100 ln 2 / 100 r

  = 70 / 100 r

  = 70 / annual interest rate

since 100 ln 2 ~ 70 and r is the annual interest as a decimal, 100r is the annual inflation as a percent. The above formula is often called the Rule of 70.  Let's consider some examples.

Example 1  Assume that the annual rate of inflation is 2.5%.  Estimate the number of years it takes for prices to double.

t = 70 / 2.5 = 28 years

It takes roughly 28 years for prices to double at an annual inflation rate of 2.5%.

Example 2  You invest your savings account at 8% annual interest.  How long does it take before that original investment will double in value using the Rule of 70?

t = 70 / 8.0 = 8.75 ~ 9 years

The online calculator below determines the time (in years) that it takes before your investment will double in value.

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