I believe BTC-E takes their cut out of the BTC you receive, so:
You would sell your 100 USD and receive 1 BTC minus 0.2% (0.998 BTC).
We want that 0.998BTC to be worth 100 USD, after the fee--which means 100USD is 99.8% of the sale price.
100 / .998 will give us the total sales price: 100.2004008...
So you would need to sell your .998BTC for roughly 100.2004USD, but we measure price in the 1 BTC = x USD format, so:
0.998 BTC is 99.8% of the ideal price of 1 BTC, which means 100.2004 is 99.8% of the price of 1 BTC.
100.2004 / .998 = 100.4012
So you would need to sell when the price is 100.4012 USD per bitcoin.
To test this:
.998 BTC * 100.4012USD = 100.2003976USD, minus .2% (100.2003976 * .998 = 99.999996... USD)
Of course it doesn't add up to exactly 100USD, because I truncated a few decimal places
You were very close in your original thinking ((100 * 1.002) * 1.002), but to be precise you have to look at it the way I outlined it above.
Alright class, if anyone has a question please raise your hand
You would sell your 100 USD and receive 1 BTC minus 0.2% (0.998 BTC).
We want that 0.998BTC to be worth 100 USD, after the fee--which means 100USD is 99.8% of the sale price.
100 / .998 will give us the total sales price: 100.2004008...
So you would need to sell your .998BTC for roughly 100.2004USD, but we measure price in the 1 BTC = x USD format, so:
0.998 BTC is 99.8% of the ideal price of 1 BTC, which means 100.2004 is 99.8% of the price of 1 BTC.
100.2004 / .998 = 100.4012
So you would need to sell when the price is 100.4012 USD per bitcoin.
To test this:
.998 BTC * 100.4012USD = 100.2003976USD, minus .2% (100.2003976 * .998 = 99.999996... USD)
Of course it doesn't add up to exactly 100USD, because I truncated a few decimal places
You were very close in your original thinking ((100 * 1.002) * 1.002), but to be precise you have to look at it the way I outlined it above.
Alright class, if anyone has a question please raise your hand