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:
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|
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:
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.