Einstein On Compound Interest (Rule Of 72)
Albert Einstein’s spirit is still being conjured up to sell the idea of compound interest / returns. The genius physicst regaled compound interest as the ninth wonder of the world. He was also credited with popularizing compound interest by introducing a simple mathematical approximation (click on picture!) :
72 divided by interest rate return = # of years it takes for your money to double.
The rule of 72 also has a cousin, the rule of 115, that helps you determine when your money may triple while earning an arbitrary interest rate.
Financial companies and advisors often use this gimmick to “open the eyes” of less sophisticated investors — your average joes. Primerica is not the only company to leverage the rule of 72 for encouraging people to pursue higher returns. Many other companies have use different derivations of the rule for their own purpose. I’ve also heard of the 7-10 rule, where if your money is earning 7% it doubles every 10 years and vice-versa. Seeing the rule of 72 can be enlightening (as it was for me), but the problem is that such information without the proper context can be very misleading too!
What Are They Not Telling You?
- The mathematical approximation is more accurate with lower interest and results diverge as the interest rate rises. (Example: If you earn at 72% interest rate, your money does not double in 1 year. It takes 100% to do that!)
- The approximation only works for interest rates, not for fluctuating rate of returns!
Surprised at the fact that the rule of 72 doesn’t work for equity returns? Let’s examine this further! But first, think about why Einstein used it for compound interest and never said compound returns. There’s a big difference! Einstein meant for the rule to be used for savings account and money market interest returns. If you want to stretch the definition, it may include interest-bearing bonds. But equity return is a totally different subject!
The Art Of Return Manipulation
When your portfolio drops from $100,000 to $50,000, it is a return of -50%. But to bring $50,000 back up to $100,000. It needs a return of 100%. When you hear advisors evoke the rule of 72 and telling you that you are better off earning 8%, 12% or more with an equity mutual fund versus a 6% interest return. Which is better? Let’s set up this case study!
Investment A: Starting capital of $100,000 earning 6% on average for 3 years. No negative returns (An average bond fund).
End of year 1: (6%) $106,000.00
End of year 2: (6%) $112,360.00
End of year 3: (6%) $119,101.60
Investment B: Starting capital of $100,000 earning 8% on average for 3 years. No Negative returns (An above average bond fund).
End of year 1: (8%) $108,000.00
End of year 2: (8%) $116,640.00
End of year 3: (8%) $125,971.20
Investment C: Starting capital of $100,000 earning 8% average for 3 years. Possibility of negative returns (Equity mutual fund).
End of year 1: (-12%) $88,000.00
End of year 2: (-2%) $84,240.00
End of year 3: (38%) $119,011.20
Slow And Steady Wins The Race!
As you can see, when you introduce the possibility for the capital to be depleted by negative returns, compounding is no longer relevant! You can see how return figures are relative to the time frame they are measured. But more importantly, losing on your original capital can create a big dent too big for a windfall return to overcome. If your portfolio value can drop, it defeats the purpose of compounding! Extend this example over longer periods (such as 10, 20 years) and you will see why investors speculating on high return mutual funds that also have wild fluctuations will not get the benefit of the rule of 72 as they expected.
The next time you meet up with your advisor and he wants to talk about the rule of 72. Remind them that it is a rule for compounding interest returns, not for compounding equity returns. Show them what you’ve learnt, and check out their reaction!
Update: I’ve been humbled by a professional — a CFA portfolio manager/analyst who pointed out the logic flaw in this assessment. You can find out what I’ve learnt here!
