What is the doubling time formula?

t = ln 2 ÷ ln(1 + r) for annual compounding, t = ln 2 ÷ [m × ln(1 + r ÷ m)] for m periods a year, and t = ln 2 ÷ r for continuous growth.

How long does it take to double money at 7%?

10.24 years with annual compounding and about 9.9 years with monthly or continuous compounding.

Why is ln 2 in the formula?

Doubling means the growth factor equals 2. Taking natural logarithms turns the exponent into a product that can be solved for t.

Does doubling time depend on the starting amount?

No. Doubling time depends only on the growth rate and compounding frequency.

Doubling Time Formula and Calculator

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Doubling Time Calculator

Doubling time is how long it takes a quantity growing at a steady percentage rate to become twice as large. In finance it tells you how long an investment takes to double; the same formula applies to prices under inflation, a customer base, or a population. Setting (1 + r ÷ m)^mt = 2 and solving for t with logarithms gives t = ln 2 ÷ [m × ln(1 + r ÷ m)].

Formula

t = ln 2m × ln(1 + r/m) continuous: t = ln 2r

Where

t: years for an amount to double
r: annual growth or interest rate, as a decimal
m: compounding periods per year
ln: natural logarithm

Calculator

Annual rate (r) (%)

Compounding

Result and step-by-step solution

Doubling time

10.24 years

Rule of 72 estimate: 10.29 years.

Periodic rate
r/m = 0.07 ÷ 1 = 0.07
Log of the growth per period
ln(1 + 0.07) = 0.06765865
Solve for t
t = 0.6931471 × 0.06765865 = 10.2448 years (10.24 compounding periods)

How to use the formula

The compounding frequency m matters only a little: at 7% a year, money doubles in 10.24 years with annual compounding, 9.93 years with monthly compounding and 9.90 years with continuous compounding, where the formula becomes simply ln 2 ÷ r. The calculator also reports the number of compounding periods, which is what you need for a spreadsheet model.

The Rule of 72 is a quick approximation to this formula; here you get the exact figure and the estimate side by side. To find how long it takes to reach any multiple, not just two, use the number of periods formula with FV ÷ PV set to your target.

Frequently asked questions

What is the doubling time formula?: t = ln 2 ÷ ln(1 + r) for annual compounding, t = ln 2 ÷ [m × ln(1 + r ÷ m)] for m periods a year, and t = ln 2 ÷ r for continuous growth.
How long does it take to double money at 7%?: 10.24 years with annual compounding and about 9.9 years with monthly or continuous compounding.
Why is ln 2 in the formula?: Doubling means the growth factor equals 2. Taking natural logarithms turns the exponent into a product that can be solved for t.
Does doubling time depend on the starting amount?: No. Doubling time depends only on the growth rate and compounding frequency.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.