Money doubling time calculator

Money saved at interest grows through compound interest, so each year adds more than the one before. At 6% a year, £100,000 becomes £200,000 in about 11.9 years. Bankers can estimate this in their heads with the rule of 72: divide 72 by the interest rate in per cent, which gives $72÷6=12$ years. The estimate is surprisingly good.

It works the other way round too. With inflation at 6% a year, money loses half of its value in roughly 12 years as well.

The calculator assumes that interest is added once a year.

How it works

The exact time and the rule-of-72 estimate are given by these formulas:

$$n=\frac{\ln 2}{\ln (1+\frac{p}{100})}n\approx \frac{72}{p}$$

Here p is the annual interest rate in per cent and n the number of years.

After n years the deposit is multiplied by 1.06ⁿ. We want that to equal two:

$${1.06}^n=2$$

We take logarithms of both sides and divide:

$$n=\frac{\ln 2}{\ln 1.06}=\frac{0.6931}{0.0583}\approx 11.9$$

The rule of 72 gives 12 years, which is not even a month and a half more than the exact answer. It works because for small rates ln(1 + x) is almost exactly x, and 100 · ln 2 ≈ 69.3. Instead of 69 we use 72, because 72 is divisible by 2, 3, 4, 6, 8, 9 and 12, and it also partly cancels out the error for typical rates around 8%. At very low or very high interest rates the rule drifts: at 1% it is out by about 3%, and at 30% by about 9%.