One half the square root of 2.....................is just the square root of 2.......over two...........if u squared that ..........u get two over four..................the square root of 2.......squared is...........2.............2 ..........squared is 4............................2/4..........is one half................two of those added................is 1...............................



started. With 1 split we have 2¹ or 2 times as much. With 4 splits we have 2⁴ = 16 times as much. As a general formula:

Said another way, doubling is 100% growth. We can rewrite our formula like this:

It’s the same equation, but we separate 2 into what it really is: the original value (1) plus 100%. Clever, eh?
Of course, we can substitute any number (50%, 25%, 200%) for 100% and get the growth formula for that new rate. So the general formula for x periods of return is:

This just means we use our rate of return, (1 + return), “x” times.