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Simple interest

The interest is calculated each time based on the same seed capital.
This is the case if you withdraw the interst as soon as it is paid.

Since the interest is directly proportional to the time unit, the following rule applies: I = S.ir.n

• I: Interest, the remuneration that a capital yields
• S: Seed capital
• ir: interest rate on which the interest depends
• n: number of periods of interest calculation / payment

The final capital (C) of seed capital (S) is equal to the sum of the initial capital and the interest.

C = S + I = S + S.ir.n = S.(1+ir.n)

Compound interest

Ater each period, the interest is added to the capital and in turn also earns interest (the interest is capitalized).
As a result it is clear that the final capital will be larger for compound interest then for simple interest.

C_n = C.(1+i)ⁿ Where C_n is the value of the capital after n periods of compound interest.

Difference between simple and compound interest

S (seed capital): $ 

ir (interest rate):   0 1 2 3 4 5 6 7 8 9 , 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9  %

n (number of periods):  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40