To find after tax real return given net return = 20% inflation= 3% tax rate=2.5% we first find after tax return (.20x(1-.25)=15%) and then find after-tax real return by [(1+.15)/(1+.03)]-1= 1.1165 – 1 = .1165

but why is that we divide 1 plus the after tax return by 1 plus the inflation rate? i feel like this is a silly question but i just cant seem to figure it out!

(First, you have a typo: you gave the tax rate as 2.5% when you apparently meant 25%.)

You divide by (1 + inf) because future dollars have less purchasing power than present dollars: less purchasing power because of inflation.

A candy bar costs $1.00 today, but will cost $1.03 next year. If you have $1.00 today and earn a net nominal return of 0%, you have a net real return of –2.9%: you won’t be able to afford a candy bar next year; you’ll be able to afford only 97.1% of a candy bar.