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No need to apologize, zzyxxyzz. When more questions arise, feel free to ask them.

For most investments, when you sell you report it on Sch D, the capital gains schedule, usually on Form 1040. So for details take a close look at the instructions for Form 1040 and Sch D.

The IRS treats each sale of whatever security as an individual transaction. Say you purchased a given stock on two different occasions and then sold some of your shares this tax year. The IRS is concerned only about the shares that you sold. You report when you sold them, the price you got for them, and what you paid for them. (You have your choice of designating which shares you sold, or with mutual funds you can report an average cost.)

So with this system, each sale is a transaction in itself. All the funds you invest are presumably previously taxed, but the IRS does not care. You only pay taxes on the profit from the transactions in this year and at capital gains rates (provided you held the investment more than 1 year). In the case of less than one year ownership, its still called capital gains, but its on a separate part of Sch D and gets taxed at ordinary income tax rates, which are higher than long term capital gains rates.

There is usually no allowance for previous history of the funds. If you sold and made a profit, you pay taxes on the profit. While you hold the shares and do not sell, no taxes are due (except for dividends paid or taxable distributions like capital gains distributions on mutual funds). If you sold and took a loss, you can write off the loss against other capital gains or up to $3K per year can be written off against your other earnings. Any loss over that $3K can be carried over and written off in future years until it has all been written off.

There are a few tax events that can change the cost basis of your investment for tax purposes. They are not so common, but one of them is to claim depreciation on an asset used for business purposes. A second is if you claim depletion allowances on assets like oil or iron ore. That usually happens on Sch E and with the publically traded partnerships. But most people do not need to worry about this aspect.
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