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.
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: Divide 75% by the number of years it took your money to double. 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%!
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.
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: Divide 75% by the number of years it took your money to double. 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%!
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.
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