Investment Doubling Time Calculator

How long to double an investment?

Doubling time is the number of years a sum takes to reach twice its starting value at a fixed annual rate. The exact answer comes from t = ln(2) / ln(1 + r), and this calculator returns it alongside the two mental shortcuts people usually reach for instead, the Rule of 72 and the Rule of 70, so all three can be read against each other rather than taken on trust.

Why Does the Rate of Return Matter So Much?

Because the relationship is logarithmic, not linear. Going from 5% to 6% cuts about 2.3 years off the wait, from 14.21 years to 11.90. Going from 14% to 15% cuts about 0.33 of a year, from 5.29 to 4.96. The same one percentage point buys seven times as much at the low end as it does at the high end, which is why the curve is steepest exactly where most long-run return assumptions sit.

Set the figures beside each other and the shape becomes visible: 2% takes 35 years, 4% takes 17.7, 8% takes 9.0 and 16% takes 4.7. Each doubling of the rate roughly halves the time, but only roughly, and the gap from that rule widens as rates climb. The compound interest material published by the US Securities and Exchange Commission sets out the underlying growth mechanics this rests on.

A Common Oversight Worth Knowing About

Charges, taxes and inflation all attach to the rate, and the rate is the only thing this calculation reads. A headline 7% carrying a 1% annual charge is a 6% input here, which moves the doubling time from 10.2 years to 11.9, so a single percentage point of cost adds more than eighteen months. Inflation works the same way: a 7% nominal return against 3% inflation is a real return of about 3.9%, which doubles purchasing power in roughly 18.2 years rather than 10.2.

Whichever rate goes in is the rate the answer describes. Entering a nominal, pre-cost figure produces a nominal, pre-cost doubling time, and that is a different question from how long real spending power takes to double.

A worked example

At the default 7% annual rate the tool returns 10.2 years, with the Rule of 72 at 10.3 years and the Rule of 70 at 10.0 years alongside it. All three answer the same question, and at this particular rate the logarithmic result sits between the two approximations, which is not true everywhere.

What moves the number most

There is only one input, and that is the point worth taking away. Doubling time depends on the rate and on nothing else: 1,000 and 1,000,000 both double in 10.2 years at 7%, because doubling is a ratio and the starting figure cancels out of it. Amount determines what a doubling is worth, never how long it takes.

That also means the tool answers a narrower question than it might appear to. It says nothing about contributions added along the way, and a portfolio receiving regular deposits reaches twice its opening balance far sooner than this figure suggests, through deposits rather than growth.

The formula behind this

Setting (1 + r) raised to t equal to 2 and taking logarithms of both sides gives t = ln(2) / ln(1 + r). That is the exact result, and it is a different expression from the Rule of 72, which is the approximation 72 / rate. The two are often spoken of together, so it is worth separating them: 72 divided by the rate is the shortcut, while the logarithm is the arithmetic that shortcut approximates. OpenStax's Principles of Finance covers the compounding machinery both expressions come from.

The model assumes one constant annual rate, annual compounding, and no deposits or withdrawals across the period.

What this doesn't capture

A constant annual return is an assumption no market obliges, and the gap it hides is larger than it looks. Volatility pulls the compound return below the average return, so two runs with the same arithmetic average double at quite different dates: a steady 7% every year doubles in 10.2 years, while a run alternating +37% and -23% averages the same 7% arithmetically but compounds at only 2.7% and takes 25.9 years. The rate this tool wants is the compound one. Costs, tax and inflation sit outside it unless they are folded into that rate before entering it. Read the figure as one scenario under stated conditions rather than a date.