"Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn't … pays it."

-Albert Einstein

There are three main variables to compound interest*: The starting dollar value, the rate of return and the amount of time. Each of these variables affect the ending dollar value in a different way.

Hypothetically, let's say you start with $10,000 to invest, get a 10% average annualized return and invest over a period of 10 years. After the 10 year period, you will end up with $25,937 - over two and half times your initial investment. Now let's say that a magical investment genie appears before you right as you are about to make your initial investment. But instead of giving you three wishes like a normal genie, he gives you the ability to choose from one of the following options:

Double your starting value from $10,000 to $20,000

Double your average annualized return from 10% to 20%

Double your total time period from 10 to 20 years

Which option should you pick if you want to maximize your ending value? (And no, he doesn't give you a calculator to help figure it out.)

Option one sounds pretty good, right? You start out with twice as much, so you should end up with a lot more. A quick calculation shows you'd end up with $51,875, or exact double the amount of money as the original calculation. That's because for compound interest, the starting dollar value has a multiplication effect. If you start out with 2 times as much, you end up with 2 times as much. And if you start out with 10 times as much, you end up with 10 times as much.

Option two also sounds good. Achieving 20% annualized return is getting near Warren Buffett level returns on investment. It's hard to attain that level of returns for long periods of time outside of the help of a genie or investment guru. In this scenario, you end up with $61,917, or about $10k more than option 1.

What about option three? Well just from the sound of it, turning 10 years into 20 years seems pretty impossible without the aid of genie or a time machine. So, if this is seemingly the hardest option to accomplish, does it also result in the most amount of money? Let's find out. By adding an additional 10 years of investing, this option yields $67,275. So yes, in this scenario, magically increasing the time adds the most value your ending investment pot.

So if you told the genie that you choose option 3, congratulations, you just maximized your investment portfolio!

Hopefully this shows that while the amount of money you start with is important, it's actually the least important variable in compound interest. Additionally, a small starting value can always be offset by just contributing more money over time. However, the earliest dollars are the most important because new dollars added later on have less time to compound.

Thankfully, you don't need a genie or a time machine to increase your investment period. In the case of retirement, either start investing sooner or delay retirement to a later date. But I really have to encourage starting as soon as possible. On top of being able to take advantage of the extra time, you may also benefit from learning early from your mistakes with a small amount of money rather than making big mistakes later on in your investment career. But better late, than never.

*Note: it gets a little more complex when one contributes more money over time or plays around with the frequency of the compounding period. So for this example, we will focus on simple compound interest (no additional contributions) and use an annualized compounding period.