Overall percentage increase

Question

If your salary increased by 10% and then after 6 months, it increased by another 10%, what is the overall percentage increase?

The answer is 21% but not sure how that's achieved.

Answer 1

Let S be the initial salary. The first increase of 10% gives a new salary S₁ of

S₁ = 1.10S,

which is 110% of S. The second increase of 10% gives a final salary S₂ of

S₂ = 1.10S₁ = 1.10(1.10S) = (1.10)² S = 1.21 S,

which is 121% of S, i.e. 21% greater than the initial salary S.