DislikedThe thing is, he's trying to calculate what his rate of return is on the money he actually used to trade with. How much he intended to use (in his mind, as you put it) doesn't mean anything because it's not in use. It's only the money actually used for trading that can be used to calculate a return. Remember, it's called a return on investment, not return on what you think you might invest.
Also, the $800 earned was not from just the first $1,000. If it was, then you'd be right at 80% return.
The first $500 he earned was from a $1,000 investment. That means he earned a 50% return on that investment:
500 / 1000 = 0.5 x 100 = 50
The balance is now $1,500.
Then, he adds another $1,000, bringing his balance to $2,500.
He makes another $300 on that balance, which is a 12% return on investment:
300 / 2500 = 0.12 x 100 = 12
Now, because there are two investments, the two returns are added together and divided by two:
50 + 12 = 62 / 2 = 31
So, his actual rate of return is 31%.
The formula at http://library.thinkquest.org/3096/42analy2.htm shows how to do it. In this case, the two periods are not years, but the principle is the same because there are two separate periods of returns to calculate.Ignored
From my rather hazy point of view here in the middle of the night, this seems to be the right approach. I will go into it tomorrow and will be back then, but this makes perfect sense to me!