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Doubling Your Money

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
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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.

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Best of: Rule of 72

A quiet day so here is one of my favorite postings from this year.

Einstein and his Rule of 72

Doubling your investment

How long to Double Your Savings based on Interest Rates

This is a rewording of a earlier posting on July 21st 2005. OK, so maybe I will concede that Einstein may have stated that this was important, but I am still not convinced he “invented” it, but be that as it may.

If you click on the graph on the right you will find a gif that will show you a graph to show you the rule of 72 at work. Assuming your saving a set amount of money with only 1 compounding period per year, this graph is fairly accurate.

The other thing to remember is this is a DOUBLING period, and the more of those the better. Why? Remember if you find an investment that grows say by 10% a year (over year), your money doubles in 7 years (about), so in 21 years (about) your money will be 8 times what it is today! (remember 2 * 2 * 2 == 8). This is why it is so crucial to find good growth in your investments.

HOWEVER, risk is another thing to take into consideration too, and we’ll talk about that soon as well.

How many years until you retire? How many doublings are you going to need to reach your retirement money goals? You may need to figure that one out very soon.

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DRIPS: It Really Works!

Given I am an Index Investor, Dividend Reinvestment isn’t really a big thing for me any more, but at the time, it did play nicely for me. Whether you should invest in companies that pay dividends (and maybe should put that money into building the company) is an argument for other folks.

DRIP : Dividend Re-Investment Programs

Early on in my investing career I got around to phoning up my stock brokers and asked to join the DRIP for every common stock that I owned and it has finally paid off!

What’s a DRIP?

Dividend Reinvesment Plans
No not that kind of Drip, Dividend ReInvestment Plans

DRIP is a Dividend Reinvestment Program, which most stocks typically offer you, so that you can buy stock with your dividend payments (instead of taking the cash). The cost of buying this stock is FREE, which is the best part, so I get more stock in something I already hold stock in AND I don’t have to pay any brokerage fees.

Doesn’t that sound like a good idea? Any left over moneys goes to my account, and typically you are only allowed to buy whole stock (i.e. you can’t buy 1.5 shares of XYZ).

The only problem I have run into, is that I usually didn’t own enough common shares to get a large enough dividend to buy a share when dividend time rolled around, but this time two of my stock came in!!! Whoo Hoo! I own 3 more shares! Not much? Well, we’ll see, but it’s a start!

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Taxes coming soon!

Taxes Coming

I keep having to remind myself of that one. I have my Quicktax installed and ready to go, but my current employer has a tradition of only sending out my T4 on February 33rd (or whenever the last day that they can is). I usually submit shortly thereafter, because my taxes are really not that complicated.I am proud to say that this year I do get to declare my income from blogging (it is a very small amount, but I am proud to say that I am a Minuscule Business now (the smallest of Businesses)). I figure for the amount of tax I have to pay, who really cares?

I plan on doing another essay on just how much my wife is worth (in the view of the CRA, not me, she is priceless to me (who would stay married to me for 20 years?)). My guess is not much more than last year, but if Mr. Flaherty does as he is thinking, and is not just teasing us, she’ll be worth a heck of a lot more!

This week in Carnivals

Blogging away Debt is hosting the 74th Carnival of Debt Reduction where she mentions my entry about whether to build up RRSP or pay down Debt.

The 87th Carnival of Personal Finance hosted by 2Million – My Journey to Financial Freedom included my discussions of Einstein’s Rule of 72  remembering, Einstein Finance.

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Einstein: Doubling is the trick!

The key to the rule of 72 is that it is describing how long it takes your money to double. The shorter the period, the more doubling periods you will get over a long period of time (if you double click on the graph beside you will see what I mean).

Doubling your investment
How long to Double Your Savings based on Interest Rates

If you look at the table below you can see what happens if you can actually get your investments to give you 7% or higher growth every year:

RateYears to DoubleGrowth over 40 years
1%69.70.0
2%35.02.2
3%23.43.3
4%17.74.8
5%14.27.0
6%11.910.3
7%10.215.0
8%9.021.7
9%8.031.4
10%7.345.3
11%6.665.0
12%6.193.1
13%5.7132.8
14%5.3188.9
15%5.0267.9
16%4.7378.7
17%4.4533.9
18%4.2750.4
19%4.01051.7
20%3.81469.8

So as you see if you can get your investments to pay 10% a year somehow, your initial investment will have grown by 45.3 as a multiple. That means if you invested $1000 (and never added to the principle), forty years later you would have $45,300 , not bad eh?

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Einstein Key to Riches ?

Of course if you could find something that paid 20% that same $1000 would be worth $1,469,800 , but who could find something that pays that much (unless you were running a pay day advance company).

No Einstein’s observation about the rule of 72 isn’t that earth shattering, it is simple arithmetic, but something to keep in mind when investing, or going into debt.

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