How do I increase x by y%, z amount of times?

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How do I increase a number by a number a specific ammounts of times using a calculator or just how?

Example: I want to increase 100 by 0.5% 3 times so 0.5% of 100 =

0.5 + 100 = 100.5

0.5% of 100.5 =

0.5025 + 100.5 = 101.0025

0.5% of 101.0025 =

0.5050125 + 101.0025 = 101.5075125

.

It would be fine up to about 5 times but i want to increase 100 by 0.5% over 100 times so I would much rather be able to do it in a single calculation.

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You are basically multiplying $100$ with $100.5\% = 1.005$. E.g. for your first calculation you get $100\cdot 1.005 = 100.5$. If you want to increase by $0.5\%$ $n$-times in a row, you can just multiply with $$ 1.005^n = \underbrace{1.005\cdot 1.005 \cdots 1.005}_{n\text{-times}} $$

For your example of $n=3$ we actually get $1.005^3=1.015075125$ giving your calculated result of $101.5075125$.

For $n=100$ you would get $1.005^{100}=1.64666849212$ resulting into

$$ 100\cdot 1.005^{100}=164.666849212. $$