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The Law of Compounding Interest

By Edited Sep 25, 2014 0 0

 

So…you’ve decided it’s time to take control of your finances.  Congratulations!  Though you’ve only taken the first steps toward financial freedom, it is important to realize that you have

Investing
already traveled further than most.  To many, personal finance can seem like a mystery – a strange, far-off land filled with silly jargon, number-letter combinations, and that steady mantra that saving today will create a more satisfying tomorrow.  But how is that tomorrow reached?  Well, in the world of personal finance, there is no tenant more important than The Law of Compounding Interest.  It is the metaphorical alpha and the omega – the key to the financial future you seek.  But I was never good at math and numbers – I’ll never be able to understand it!  But that’s where you’re wrong.  You don’t need to be a mathematician to understand this simple principle.  Let’s take a look.     

The Law of Compounding Interest states that by investing your money at a certain yearly rate, not only will your initial investment grow at the predetermined percent, but the yield from your initial investment will grow at that rate as well.

Make sense?  Hmm…it was a tad bit finance-y.  How about an example:

To start off, let’s pretend it’s your birthday. 

…happy birthday.

Since they love you so much and can’t believe their little boy is already [insert age here], your parents decide to hold a dinner in your honor.  At the dinner, there’s all sorts of good stuff – steaks, grilled asparagus, those little cupcakes that have M&M’s baked into the frosting.  Yeah…it’s pretty much the best.  They’ve invited your entire extended family to this event, including your long-lost, Great-Aunt Bertha.  You know, the one with the abundance of teal eye shadow?  Married to your dad’s Uncle Steve with the parrot?  Well…it doesn’t matter.  She was there.  And since she was there, as a way to make up for all the birthdays she’d missed, Aunt Bertha gave you a crisp check for $100.

Yahtzee.

However, rather than going out and buying a fresh new pair of kicks or a couple hundred gumballs, you decide you are going to invest your windfall.  You look around, do a little research, and find a nice ETF (Exchange-Traded Fund – essentially, an index-fund that trades on the stock exchange) that mimics the movements of a broad-based market – say, large-cap U.S. equities.  Since your life is already pretty much a fairytale (sweet steak dinners, surprise Benjamins from distant relatives), you’re hardly surprised to learn that the ETF you’ve set your sights on is currently priced at exactly $100.  You buy a share, hit the fridge for leftovers, and then call it a day.

Now, for the sake of simplicity in this example, let’s assume that your ETF returns 7.0% a year, every year.  It should be noted that, if taken on average, this is not an unrealistic assumption.  The large-cap U.S. equity market has averaged a return in this ballpark over its lifetime.  The difference between our example and reality is the manner in which the 7.0% is achieved.  While in our example we will assume a 7.0% return every year (7.0% in year one, 7.0% again in year two, 7.0% again in year 3…we think you get the picture), in reality, the 7.0% would only be your average return.  You could return 9.0% in year one; 4.0% in year two; (2.0%) in year three, etc.  Over enough time, the return would eventually average out to about 7.0% a year. 

Got it?

Cool.

So, for the sake of simplicity, your ETF returns 7.0% every year.  After one year (dare we say, one amazingly spectacular year), you think of your Great-Aunt Bertha’s generosity – in both the giving of gifts and the application of make-up – and you decide to check in on your ETF.  When you pull it up on your computer, you see that the $100 ETF you bought has appreciated to $107 – growth of $7.00 (7.0% of $100).  You smile, pat yourself on the back, and then walk away from your computer.  Flash forward one year later.  Again, you think of your Aunt Bertha’s generosity and head over to the computer to check your ETF.  But in year two, rather than appreciating by $7.00 like in year one, your ETF has instead grown $7.49 (7.0% of $107).  And in year three, it grows $8.01 (7.0% of $114.49).  See the pattern here?  Through the Law of Compounding Interest, it isn’t only your initial investment ($100) that grows at the 7.0% rate each year, but your initial investment plus whatever earnings through interest you’ve accrued.  So – keeping this principle in mind – if you were to hold that ETF for 40 years, it would not be worth $380 at the end of the period ($100 + $7 a year over 40 years), but rather $1500

Financial success
Understanding the Law of Compounding Interest is a fantastic foundation to a fun-filled future of financial freedom.  In conclusion – we have three bits of advice.  First – invest early.  If the Law of Compounding is a finely made German automobile, time is its fuel.  Give your investments enough time, and you’ll be amazed how far they’ll take you.  Second – invest often.  A penny saved may be a penny earned, but (as you saw above) a penny invested is a nickel and a dime.  Save all the pennies you can, invest all the pennies you save, and have patience.  There is no simpler formula to financial success.  And finally, invite your Great-Aunt Bertha around more often.  That lady gives one heck of a gift.
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