I don't really understand what you mean...

But if it helps...

Compound interest can be written as a series of recursive simple interest functions with interest being charged on interest in each time period. This can then be converted to a closed form, which you know as the compound interest formula.

You should know the simple interest formula

so the amount accumulated is

.

If we assume that we recalculate the simple interest every time period, then and we can rewrite as a new principal for the next calculation.

So...

.

.

.

.

I think you can now see that after time periods, the amount accumulated equates to

, with .