Doubling Your Money

in Einstein, Investments

One of my first real articles I wrote when I started out was Rule of 72 (more Einstein Finance). I wrote 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:

Rule of 72 Graph
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.

{ 5 comments }

  • Jason May 24, 2014, 12:20 PM

    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…

    Reply
  • LifeInsuranceCanada.com May 22, 2014, 9:49 AM

    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”.

    Reply
    • bigcajunman May 22, 2014, 9:52 AM

      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.

      Reply
  • debt debs May 22, 2014, 9:42 AM

    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.

    Reply
  • Asset-Grinder May 21, 2014, 5:21 PM

    The rule of 72 is great tool for dividend growth stocks I find cause of the real returns of dividends. Great recap !!!

    Reply

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