Challenge Level

If a sum invested gains $10\%$ each year how long will it be before it has doubled its value?

If an object depreciates in value by $10\%$ each year how long will it take until only half of the original value remains?

**Why aren't these two answers the same?**

Is there a rate, used for both gain and depreciation, for which those two answers would actually be the same? How do you know?

*If this problem caught your interest and you know some Stage 5 mathematics, this Plus article on Carbon Dating could be a good next step for you.*