I believe you mean, how is the equation derived. It is actually quite simple. Every time you add (for example) 5%, the capital increases by a factor of 1.05. This factor is calculated as 1 + 5/100, in this example. Multiplying repeatedly by this factor is equivalent to raising the factor to a power. For example, in 4 years, and assuming an initial capital of 1000, you get 1000 x 1.05 x 1.05 x 1.05 x 1.05, which is the same as 1000 x 1.054.
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If the rate of annual interest is r% the period is n years and the amount invested is y Then the compound interest is y*(1+r/100)^n - y
S=P(1+r)^n
A=Pe^rt A=Total Invested P=Principal r=Rate t=time
With compound interest, the interest due for any period attracts interest for all subsequent periods. As a result, compound interest, for the same rate, is greater.With compound interest, the interest due for any period attracts interest for all subsequent periods. As a result, compound interest, for the same rate, is greater.With compound interest, the interest due for any period attracts interest for all subsequent periods. As a result, compound interest, for the same rate, is greater.With compound interest, the interest due for any period attracts interest for all subsequent periods. As a result, compound interest, for the same rate, is greater.
compound interest increases interest more than simple interest