Net salary with progressive or flat tax

Text

Compute the net salary over $12$ months of a person with gross income $35$$ in the two cases:

• (a) progressive bracketed tax: $10\%$ from $0$ to 10\$$; 25%$from$10$to$23$$;$35%$above$23$$;
• (b) flat tax at $20\%$.

Solution

(a) Progressive on 35\$$: $$T=10\%\cdot 10+25\%\cdot(23-10)+35\%\cdot(35-23)=1.00+3.25+4.20=8.45\. Net yearly $=35-8.45=26.55\; monthly $=\dfrac{26.55}{12}\approx2.21$$.

(b) Flat: T=20\%\cdot35=7.00\$$. Net yearly =28.00$$; monthly$=\dfrac{28}{12}\approx2.33$. $$\boxed{\ \text{(a) net monthly}\approx2.21\;\qquad \text{(b) net monthly}\approx2.33$\ }$$