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Doubling Your Money

One of my first real articles was about the Rule of 72 (more Einstein Finance). The Rule of 72 is a simple heuristic for figuring 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 (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).



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
12% or higher and doubling in less than 6 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:

Rule of 72 Graph
Simple Rule of 72 Graph

This is a straightforward model, given very few folks dump a load of money into a single investment and let it grow with no intervention. Still, 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 handy model to remember.

Feel Free to Comment

  1. I remember when I first learned the rule of 72. It was comparable to my fascination of ants. Seriously, a colony of ants is quite amazing. Did you know they even build a landfill for all of their waste? Those little guys are quite intriguing…

  2. The last time I was in the MathSoc office at University of Waterloo (and that was a looong time ago) the Natural Log was gone, replaced by an empty box of Tide, with a sign that said something like “Natural Log, recycled”.

    1. The office has moved I believe as well. I was a Computer Science Club member, so we looked across the hall at MathSoc a great deal. The CSC was the cooler place to be, I always thought.

  3. Very clear! Thanks for facilitating my financial education.

    So if I take my current investment portfolio and say I’m earning 8%, it will double in 9 years. Now I need to check if I’m getting that rate of growth. I’m still contributing also.

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