Power of Compounding – The Doubling Cycle

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Personally, I think the “Power of Compounding” is probably the single, most important concept of personal financial planning. The power of compounding is the engine that grows your assets into wealth.

The power of compounding is the concept that the returns you make in one year get compounded in each subsequent year so your money grows over time. This is where you might hear people say, if you started out with $10,000 today and earned a 7% return on your money, you would have $320,000 in 50 years. However, thinking about 50 years (or 40, 30,  or 20 years for that matter) and the impact each year makes is kind of difficult to wrap your head around. So I like to think of compounding in terms of “doubling cycles”, as I will explain below.

To make it easier to follow, for all of the examples below, we will assume that our average rate of return is 7.2% (for ease of calculation too, as you will see below).

Note: We will have a separate post on determining your average rate of return target. In short, most brokerage firms/advisors recommend an asset allocation model based on your risk profile. There are plenty of sites with questionaires that help you determine what kind of risk profile you are. Here are a couple. CNN/Money has a simple three question wizard. Schwab has a more extensive questionaire.  In Schwab’s profiles, a Conservative allocation has a historical average return of 7.8% and an Aggressive allocation has a histroical average return of 10.3% (but it also has a higher and lower loss range in any given year).

The Very Basics of Compounding

Briefly, the basic concept of compounding is that you will get a return on your money (like interest on your savings account) every year. In the second year, you will get a return on your original investment as well as the return you made in the first year. In the third year, you get a return on the total of the original investment, the first year’s return, and the second year’s return. This continues and keeps growing with each year. A numerical illustration:

Original investment = $10,000

Your money at the end of:

Year 1 = $10,000 + annual return ($10,000 * 7.2%) = $10,000 + $720 = $10,720

Year 2 = $10,720 + annual return ($10,720 * 7.2%) = $10,720 + $772 = $11,492

Year 3 = $11,492 + annual return ($11,492 * 7.2%) = $11,492 + $827 = $12,319

And so on…

Investopedia also has a good basic explanation and illustration of the concept.

You can see that looking at each individual year can be rather tedious. Fortunately, there are ways to simplify this.

The “Rule of 72”

The “Rule of 72” is a nice, easy rule-of-thumb to figure out how many years it will take for your money to double. You simply divide 72 by your average rate of return to calculate the number of years it will take for your money to double. A numerical illustration:

Average rate of return = 7.2%

Years to double = 72 / 7.2 = 10 years

The “Doubling Cycle”

In the numerical illustrations, our money doubles every 10 years. I call this our “doubling cycle”.

I think by using the doubling cycles, it is easier to understand the true power of compounding. This is what happens to your money with each progressive doubling cycle (DC) in the Table below:

Original investment = $1

DC 1 = $1 * 2 = $2

DC 2 = $1 * 2 * 2 = $4

DC 3 = $1 * 2 * 2 * 2 = $8

DC 4 = $1 * 2 * 2 * 2 * 2 = $16

DC 5 = $1 * 2 * 2 * 2 * 2 * 2 = $32

DC 6 = $1 * 2 * 2 * 2 * 2 * 2 * 2 = $64

DC 7 = $1 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = $128

As you can see, your money grows at an exponential rate with each progressive doubling cycle.  It is not straight-line linear; you don’t just double your original investment each cycle, you are earning your returns on your returns.  Sorry to get all math on you, but a simpler way to write this is 2 to the nth power  for each doubling cycle (DC 1 = 2^1 = 2, DC 2 = 2^2 = 4, DC 3 = 2^3 = 8, etc.). This is the power of compounding.

You can now think of number of doubling cycles you have left and the corresponding doubling multiple. In this example, if you are 45 years old with $500K in your portfolio and you want to retire at age 65, then you would have two doubling cycles left (20 years = two 10-year doubling cycles) and would estimate that your $500K portfolio would grow to $2M ($500K * 4; DC 2 in the table above). Likewise, if you are 25 years old, you will have 4 doubling cycles (40 years = four 10-year doubling cycles) and would retire with an estimated $8M ($500K * 16; DC 4 in the table above). Now it’s pretty easy to look at what you have and quickly determine how much your current portfolio will be when you retire (note: this would be more of a floor, as you will be adding additional savings to your portfolio while you are working).

A Powerful Argument for Starting Early

Conceptually, we all know that the earlier you save and invest, the better. But what difference does a few years make (you know, the “I’ll start saving next year” excuse)?

Let’s think of this in terms of the doubling cycle. We know that if we start earlier, we have more doubling cycles in our potential investment horizon. Conversely, we have fewer doubling cycles the later we start our investment program. In other words, there is an inverse relationship between the years we delay and the number of doubling cycles. So let’s reverse the order of the Doubling Cycle Table and see what we have:

Yrs Delay          Doubling Cycle          Difference btwn Cycles

Few                    DC 7 = 128x

.                          DC 6 = 64x                                 -64x

.                          DC 5 = 32x                                 -32x

.                          DC 4 = 16x                                 -16x

.                          DC 3 = 8x                                   -8x

.                          DC 2 = 4x                                   -4x

Many                 DC 1 = 2x                                   -2x

End date           Retirement age                         -1x

If you start when you are very young, you might have the potential to achieve the DC 7 level (2 to the 7th power = 128), or 128x your original investment over your time horizon. Now, if you waited one cycle to DC 6, you would be worse off by -64x your original investment. If you waited another cycle to DC 5, you’d be worse off by -32x. If you waited another cycle to DC 4, you’d be worse off by another -16x. And so on until the first cycle DC 1, where you are only earning double your original investment, which is -126x your original investment less than if you met your max potential DC 7 tier.

Back to our numerical example above using the 10 year doubling cycle from a 7.2% annual return… This is where people say, if you (more likely your parents on your behalf) invested $10,000 when you were very young and had 7 doubling cycles, you would be a millionaire by the time you retire ($10,000 * 128 = $1,280,000). More realisticlly, if you started your investment when you were 25 years old, your hypothetical max potential would be 4 doubling cycles at age 65 (40 years with a 10 year doubling cycle = DC 4 = 2 to the 4th power = 16x) and that initial investment would turn into $160,000 ($10,000 * 16). If you waited until you were 35 years old, you would have lost the DC 4 tier and dropped down to the DC 3 tier (2 to the 3rd power = 8x). Your $10,000 would now only grow to $80,000 – this delay just cost you $80,000 (your top potential tier). If you waited until you were 55 to start, your $10,000 would double only once to $20,000. It’s better than nothing, but it’s far less than $160,000.

So what does this tell us? It tells us that whatever the max potential number of doubling cycles you may have, the best, most valuable (or “most expensive” if you are a glass half empty kind-of-guy) tiers come off the board first. If you wait too long, you could end up only having 2-4x your money, rather than 8-64x your money. That is indeed a very costly mistake. That’s my doubling cycle argument for starting early. So start your financial engine now!

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