An equity interest is a proportion of ownership, typically via investment in a business. Stocks are also known as equities. Also, there is an accounting concept called owner's equity. One person might own 90% of a business, and the other 10%.
Note that bonds represent cooperation debt, while stocks represent ownership or equity interest.
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Compound interest
Simple interest is interest paid on the original principle only, Compound interest is the interest earned not only on the original principal, but also on all interests earned previously.
If the interest is reinvested and so itself gains interest (in the next interest period) it is compound interest.
It is interest on simply the original capital. After the first period, compound interest involves interest on the interest earned in previous periods and soit not simple.
There is simple interest and there is compound interest but this question is the first that I have heard of a simple compound interest.