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If I improve at something 1% daily what will be my overall improvement after 1 year?

What is the formula to calculate this?

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closed as off-topic by The Count, Paul Frost, Xander Henderson, Lee David Chung Lin, Leucippus Jul 1 at 2:04

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  • $\begingroup$ Do research on the concept of compound interest. That might help. $\endgroup$ – Michael Rybkin Jun 30 at 1:29
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    $\begingroup$ The result depends : leap year or not ? $\endgroup$ – Claude Leibovici Jun 30 at 4:19
  • $\begingroup$ Thanks Claude :) $\endgroup$ – Dercni Jun 30 at 20:02
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If your current "stock of talent" is $k_{0}$, your stock of talent tomorrow will be $k_{1}=k_{0}(1+0.01)$. Starting from tomorrow's stock $k_{1}$, your stock of talent after an additional day of improvement will be $k_{2}=k_{1}(1+0.01)$. But this is just $k_{2}=k_{0}(1+0.01)(1+0.01)=k_{0}(1+0.01)^2.$ More generally, your stock of talent after $t$ periods of improvement will be $k_{t}=k_{0}(1+0.01)^t$.

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