One of my first real articles I wrote when I started out was Rule of 72 (more Einstein Finance), where I talked about the Rule of 72, which is a simple heuristic on trying to figure out when your money can double in value, given a specific (compounding) growth rate.

Let’s make sure we are clear, the model I am working from assumes:

• I am putting an amount into a savings vehicle, and not adding any more (so the model is flawed already but stay with me on this)
• The rate of return stays the same throughout the period of time (again flawed)

When I say doubling, based on those assumptions, it is when the initial investment is now worth twice what it was initially.

I attempted to clarify my initial post with a very grainy looking graph in Einstein: The Rule of 72 a few years later, but I think we can do better than that now.

First a simple table following the formula:

$T = \frac{\ln(2)}{\ln(1+r)}$

Where T is the number of period and r is the interest rate compounded in that period, and the ln() function is the Natural Log (mascot of the University of Waterloo MathSoc as well).

 Rate (r) Period to Double (T) in years 0.50% 139.0 1.00% 69.7 1.50% 46.6 2.00% 35.0 2.50% 28.1 3.00% 23.4 3.50% 20.1 4.00% 17.7 4.50% 15.7 5.00% 14.2 5.50% 12.9 6.00% 11.9 6.50% 11.0 7.00% 10.2 7.50% 9.6 8.00% 9.0 8.50% 8.5 9.00% 8.0 9.50% 7.6 10.00% 7.3 10.50% 6.9 11.00% 6.6 11.50% 6.4 12.00% 6.1 12.50% 5.9 13.00% 5.7 13.50% 5.5 14.00% 5.3 14.50% 5.1 15.00% 5.0

Simple calculation isn’t it? You can see that it doesn’t take long to go from taking 135 years to double your investment to 15 years to double your investment (0.5% to 4.5%), but it is easier to see in a graph how this all works:

Simple Rule of 72 Graph

This is a very simple model, given very few folks just dump a load of money into a single investment and let it grow with no intervention, but it is worthwhile to understand that when someone talks about getting a 4.0% growth on their investment, that means their investment will double in 18 years (or so). It is a very useful model to remember.