# A New Year's Wish -- Calculating Really High Returns

## Jan 1, 2009

Happy New Year! Today’s post is about an easy way to quickly estimate annual return for very high returns over several years, without needing a calculator. My New Year’s wish to you is that this will actually be useful to all of you, and soon.

Actually, the exact return is 2.83%, because of the “miracle of compound interest.” What’s happening is that the original amount you invested gets a little bigger each year. Your starting investment balance for Year 2 isn’t the, say, $100.00 you started with, but $102.83, and it goes up to $105.75 for Year 3, etc. But the 3% return you calculated in your head is pretty close.

But the

But there’s still a calculator-free way to estimate the return:

Here’s another example: your money increases 8-fold in 15 years. That means your money doubled exactly 3 times (2 x 2 x 2 = 8), so it doubles every 5 years (15 years ÷ 3 doublings). So your estimated return is 15% (75% ÷ 5 years). The exact calculated return is 14.87%.

May this subject be relevant to us all!

*Low*returns are easy to calculate. Just divide the percentage increase by the number of years. For example, if your 5-year return was 15%, an estimate of 3% (15% ÷ 5) is pretty close.Actually, the exact return is 2.83%, because of the “miracle of compound interest.” What’s happening is that the original amount you invested gets a little bigger each year. Your starting investment balance for Year 2 isn’t the, say, $100.00 you started with, but $102.83, and it goes up to $105.75 for Year 3, etc. But the 3% return you calculated in your head is pretty close.

But the

*miracle of compound interest*means the above method doesn’t work for high returns. For example, suppose your money*tripled in 5 years*. The above method – divide the 200% return by 5 years – gives you a 40% annual return. But that’s not very close to the 24.6% that’s the correct number.But there’s still a calculator-free way to estimate the return:

*. In the above example, tripling your money means it doubled a little more than 1.5 times. Since the time period was 5 years, that means your money roughly doubles every 3 years (5 years, divided by slightly more than 1.5). Now we divide 75% by 3, and get 25%!***Divide 75% by the number of years it took your money to double**Here’s another example: your money increases 8-fold in 15 years. That means your money doubled exactly 3 times (2 x 2 x 2 = 8), so it doubles every 5 years (15 years ÷ 3 doublings). So your estimated return is 15% (75% ÷ 5 years). The exact calculated return is 14.87%.

*Not bad for an estimate!*May this subject be relevant to us all!

*“Painting with Numbers” is my effort to get people talking about financial statements and other numbers in ways that we can all understand. I welcome your interest and your feedback.***Related Blogs**

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