Tenfold Growth Rule Formula

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For compound interest, I know a rule of thumb for how long it takes for an amount to double is to take it's annual % of growth and divde 100 by it. For example, 25% annual growth will double in 4 years.

What is a rule of thumb calculatin for an amount to go up by an order of magnitude. So $4,000 to be $40,000?The rule of thumb for calculating the time it takes for an amount to grow by an order of magnitude (i.e., to increase tenfold) in the context of compound interest is similar to the Rule of 72 for doubling. This rule of thumb involves the natural logarithm (ln) of 10 (since increasing tenfold means multiplying by 10).

Here's the calculation:

[ \text{Years to increase tenfold} \approx \frac{100 \cdot \ln(10)}{\text{Annual Growth Rate (%)}} ]

Since (\ln(10) \approx 2.3026), the formula simplifies to:

[ \text{Years to increase tenfold} \approx \frac{230}{\text{Annual Growth Rate (%)}} ]

For example, if the annual growth rate is 25%, the calculation would be:

[ \text{Years to increase tenfold} \approx \frac{230}{25} \approx 9.2 \text{ years} ]

So, at a 25% annual growth rate, it would take approximately 9.2 years for an amount to grow tenfold.

Tenfold Growth Rule Formula created at Tue Jan 20 1970 21:38:40 GMT+0000 (Coordinated Universal Time)