doubling at 12%
- Annual growth rate
- 12%
- Multiply by
- 2
Years required6.12
DRV-006 verified table
Open this exampleFinance & Loansinterest
Money Doubling Time Calculator
How long money takes to double, triple or reach any multiple at a given rate. The general form of the Rule of 72.
Also called: time to double investment, money doubling calculator.
Years required
6.12
At 12% a year, money multiplies by 2 in 6.12 years.
Method and background
This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.
How this is calculated
Solving (1+r)^t = k for t gives ln(k) over ln(1+r). Setting k to 2 recovers doubling time; the Rule of 72 is the small-rate approximation of that special case.
t = ln(multiple) / ln(1+rate)- k
- The multiple you want
- r
- Annual rate (decimal)
Worked examples
Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.
tripling at 10%
- Annual growth rate
- 10%
- Multiply by
- 3
Years required11.53
ln(3)/ln(1.1)
Open this examplea multiple of 1 takes no time
- Annual growth rate
- 10%
- Multiply by
- 1
Years required0
degenerate case
Open this exampleFrequently asked questions
- What is the exact formula for doubling time?
- ln(2) divided by ln(1 + r), which is where the rule of 72 comes from as an approximation. At 7% that is 0.6931/0.0677 = 10.24 years.
- How long does tripling take?
- Replace ln(2) with ln(3). Tripling takes about 1.585 times as long as doubling at any rate, so anything that doubles in ten years triples in just under sixteen.