Real rate and inflation

Statement

A capital is invested for one year at a nominal rate of $9\%$. In the same year inflation is $3\%$. What is the real rate of return?

Solution

The real rate accounts for the loss of purchasing power: $r_{real} = \frac{1 + i}{1 + f} - 1 = \frac{i - f}{1 + f} = \frac{0{.}09 - 0{.}03}{1{.}03} \approx 0{.}0583 = \boxed{5{.}83\%}.$