Understanding Percentages Over Time

We expect to grow 20 percent a year, so in five years we will double our gross revenue. – Name Withheld

This is a quote from a person calling themselves a financial planner*.  I wish I were kidding.

This is not how percentages work over time.  Here’s how most people think through this:  I plan to double in five years, which is a 100% increase.  One hundred divided by five is 20.  Therefore, I will grow 20% per year.  Done!

Which is so, so wrong.  Let’s think through this.  I plan to start the year with, say, $100K in last year’s revenues.  I increase my revenues by 20% for the first year.  That means, at the end of the year, you’ve earned $120K for the year.  Congratulations!  Now, let’s see what happens next year…

Ok, you start with $120K in previous years revenue.  Now I increase my revenues by 20%.  Yay!  That means, for the year, I’ve made $144K.  You’ll notice the increase in year two is $24K, but the increase in year one is $20K.  That’s called compound interest.

$100K at 20% over 5 years

You’ll notice our financial planner pal meets their goal in the fourth year.  (I have it at year 3.8, to be precise.)  This is why financial planners and finance authors get so excited about compound interest.

If you have some trouble getting the concept the first time through it, keep trying.  I didn’t fully understand compund interest the first time I ran into it, either.  With a little work, you too can avoid this easy error.

* It was as reported to me by a financial planning magazine (which shall remain nameless), which sent an advertising email to me from a broker dealer (which shall also remain nameless).  I’m hoping they misheard the planner I’m quoting, because it’s tremendously embarassing.

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