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If I purchase $1000 worth of stock, and in the first week the stock value goes down to $900 and then in the second week the value of the stock reaches $1002, and then I sell the stock,
I am assuming (1) that you bought the stock for $1000 (a long position, not a short position), (2) you are discussing selling the stock after two weeks (a short term profit), and (3) US tax laws apply.
If you were to sell the stock at this point, your taxable profit would be $2; you would not pay tax on the $1000 originally invested.*
The simplest pro in this situation is you would collect your gain. The simplest con is that your transaction costs (mainly the broker's commission) probably is more than the profit.
Whether this would all be beneficial for you is a question you ought to ask your financial advisor (professional or not).
* A short term profit is taxed at your ordinary income rates. In the US this presently varies from 10% to 39.6%, exclusive of phase-outs.
I upvoted @CodesWithHammer, but just or clarify a point or two:
One: The fact that the stock fell to $900 between you bought it and when you sold it is irrelevant. Your profit (or loss) on a stock sale is the price when you sold it minus the price when you bought it. What it was in between those two dates makes no difference to anything.
Likewise, your tax liability depends on your actual profit, the sale price minus purchase price.
Two: You pay taxes on your net profit. Under current US tax law, if you sell stock less than one year after you bought it, this is considered a "short term capital gain" and is taxed at the same rate as normal income. If you hold it longer than a year before selling, it is a "long term capital gain" and is taxed at a much lower rate.
