From a yearly growth factor to a monthly one, why can't I just divide by 12?

Hi Arnout, Your instinct is good, you already spotted that the first attempt gives a number smaller than 1. That's the clue to the whole thing. A growth factor is a ratio, not an amount. Two months of growth means multiplying twice: 1.06 would have to become g × g. So going from a year to a month is not dividing, it's taking a root. You need the g for which g^12 = 1.06, and that's exactly 1.06^(1/12) ≈ 1.00487. Dividing 1.06 by 12 treats the factor as if it were an amount you can split into twelve pieces, and that's where it falls apart. Your second attempt is more interesting, because it nearly works. Splitting 6% into twelve pieces of 0.5% assumes the interest is always calculated over the original amount. But in month 2 you also earn 0.5% over the 0.5% that was added in month 1, and in month 3 over both, and so on. Those extra bits add up to roughly 0.17 percentage points, which is exactly your 0.0017. So it's not rounding, it's interest on interest. You can see how bad the approximation really is by making the numbers big. Take 100% per year. Divide it into twelve pieces: 8.333% per month, factor 1.08333. Then 1.08333^12 ≈ 2.61, while a doubling should give 2. Way off. At 6% the error is small because the rate is small, which is why the shortcut looks almost fine and hides the mistake. The rule I use for any problem like this: year → month: take the 12th root, so 1.06^(1/12) month → year: take the 12th power, so 1.00487^12 always check by raising your answer back to the power and seeing whether you land on the number you started with That last step is the one that saves you on an exam. If you'd tried 1.005^12 and seen 1.0617 instead of 1.06, you'd have known straight away that 1.005 wasn't the answer, which is basically what you did already. Carmen