How Much Capital You Need: the 4% Rule

Finds how much capital is needed to live off withdrawals. Drawing 4 per cent a year means 25 times the annual spending. From the capital already held and the yearly contributions, it also gives the years until that target is reached.

This finds how much capital is needed to live on withdrawals from it. Fix a withdrawal rate and the target follows directly from the annual spending.

T = \dfrac{S}{w}

Here $S$ is the annual spending, $w$ the withdrawal rate and $T$ the capital required. A rate of 4 per cent means multiplying the annual spending by its reciprocal, 25.

Where the 4 per cent comes from

Studying historical returns on stocks and bonds over thirty-year windows, researchers found that withdrawing 4 per cent of the capital in the first year and raising the amount with inflation thereafter left the portfolio intact for thirty years in almost every window tested. The work is known as the Trinity study.

That is the origin of the number. It rests on past American markets and does not transfer unaltered to every country or every period.

Years to reach the target

Given the capital already held and the yearly contributions, the tool also gives the time to reach the target.

n = \dfrac{\ln \dfrac{T + C / r}{A + C / r}}{\ln (1 + r)}

Here $A$ is the capital held now, $C$ the annual contribution and $r$ the expected return. Both the existing capital and the stream of contributions grow by the same factor $(1 + r)^n$ , so adding the contribution divided by the rate to the capital collapses the two into a single exponential.

Worked example

Spending 3,000,000 a year, withdrawing at 4 per cent, holding 10,000,000 and adding 1,500,000 a year at an expected 5 per cent, the target is 75,000,000 and it is reached in about 19.8 years.

The target is 3,000,000 ÷ 0.04 = 75,000,000, which supports withdrawals of 250,000 a month.

Points to watch

Enter spending as it really falls, tax and social insurance included. Leaving them out understates the target.

Inflation raises the cost of the same life over time. It is safer to work in real terms, using a return with inflation already subtracted: a nominal 7 per cent against 2 per cent inflation means entering 5.

The order of returns matters as well as their average. A sharp fall in the first years of drawing down empties the capital faster than the same average return arriving in a kinder sequence.