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.
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There is simple interest and there is compound interest but this question is the first that I have heard of a simple compound interest.
There is no carrot in the compound interest formula!
Compound interest
It depends on which compound interest formula you mean. Refer to the Wikipedia Article on "Compound Interest" for the correct terminology.
The effect of compound interest is that interest is earned on the accrued interest, as well as the principal amount.