# Calculating my improvement via daily compounding [closed]

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

What is the formula to calculate this?

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

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• Do research on the concept of compound interest. That might help. – Michael Rybkin Jun 30 at 1:29
• The result depends : leap year or not ? – Claude Leibovici Jun 30 at 4:19
• Thanks Claude :) – Dercni Jun 30 at 20:02

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 $$k_{t}=k_{0}(1+0.01)^t$$.