The "rule of 72" says that if you divide the 72 by the percentage rate, it gives the approximate number of years for the investment to double.

Here is a table showing those values

% 72/% actual value

1 72 2.047099312

2 36 2.039887344

3 24 2.032794106

4 18 2.025816515

5 14.4 2.018951594

6 12 2.012196472

7 10.3 2.005548375

8 9 1.999004627

9 8 1.992562642

10 7.2 1.98621992

20 3.6 1.927757874

30 2.4 1.876999019

50 1.44 1.792963353

So it's actually pretty close.

The formula for the last column (actual value after 72/P years) is V = (1+P/100)^(72/P)

where P is the percent.

Here is a table showing those values

% 72/% actual value

1 72 2.047099312

2 36 2.039887344

3 24 2.032794106

4 18 2.025816515

5 14.4 2.018951594

6 12 2.012196472

7 10.3 2.005548375

8 9 1.999004627

9 8 1.992562642

10 7.2 1.98621992

20 3.6 1.927757874

30 2.4 1.876999019

50 1.44 1.792963353

So it's actually pretty close.

The formula for the last column (actual value after 72/P years) is V = (1+P/100)^(72/P)

where P is the percent.