It's a well known fact the Indians sold Manhattan for $24 dollars in 1626. Most of us learn this story in elementary school and are thought that it was ridiculous for the Indians to sell Manhattan for such a low price. I distinctly remember whenever someone in my class had been silly with money we would recite this fact to them.

But was it really as bad a deal as it sounds? What if the Indians had taken the $24 and invested it. How much could they realistically expect to have today? In order to answer this we're going to need the formula for compound interest, which can be worked out as follows:

Current Value = Past Value (1 + i)^{n}

What this equation is saying is that the amount of money today is equal to the value then multiplied by 1 plus the interest rate to the power of the number of years between now and then. The current year is 2010 and Manhattan was sold in 1626, so that means interest would have been accumulating for 384 years (2010-1626).

If we now assume that the Indians were quite astute and able to achieve an interest rate of 8% for the entire 384 years, or equation looks like this:

Current value = $24(1+0.08)^{384}

Working this equation out using a calculator shows us that if the Indians had invested the money until today they would have $164033801073221 dollars, which is clearly a phenomenal amount of money. In fact this is 164 trillian dollars, which is more than the value of all the real estate in Manhattan put together!

I hope that you find this fact as amazing as I do. I hope you can also see that time plays a vital role in compound interest. The longer you leave your money the more you will have. None of us are able to wait 300+ years to see the return on our investment, but this example hopefully makes you realise that the time to start saving is now because time plays such a vital role in the accumulation of wealth through compounding. You can adapt the equation shown above to suit your own circumstances, adjusting the amount, the number of years, and the interest rate, to see how much money you end up with under different circumstances. Remember that time plays a vital role in investment returns, so the time to start saving is now, so you can experience the magic of compound interest.