: If Joe can earn a return of $5\%$ over the next year, and inflation is expected to be $2\%,$ what is his real rate of return $($increase in purchasing power$)?$ Please do the calculation using both the theoretically correct approach and the approximation approach.

Fisher effect theoretically correct approach: $(1+$ R$)=(1+$ r$)(1+$ h$)$

Approximation approach: R $=$ r $+$ h

Where

R $=$ nominal return

r $=$ real return

h $=$ inflation premium