## Real interest rates

 Main article: Real interest rate

As was shown in the section above on the real growth rate,

${\displaystyle 1+r_{t}={\frac {1+g_{t)){1+i_{t))))$

where

${\displaystyle r_{t))$ is the rate of increase of a quantity in real terms,
${\displaystyle g_{t))$ is the rate of increase of the same quantity in nominal terms, and
${\displaystyle i_{t))$ is the rate of inflation,

and as a first-order approximation,

${\displaystyle r_{t}=g_{t}-i_{t}.}$

In the case where the growing quantity is a financial asset, ${\displaystyle g_{t))$ is a nominal interest rate and ${\displaystyle r_{t))$ is the corresponding real interest rate; the first-order approximation ${\displaystyle r_{t}=g_{t}-i_{t))$ is known as the Fisher equation.[1]

Looking back into the past, the ex post real interest rate is approximately the historical nominal interest rate minus inflation. Looking forward into the future, the expected real interest rate is approximately the nominal interest rate minus the expected inflation rate.

## Cross-sectional comparison

Not only time-series data, as above, but also cross-sectional data which depends on prices which may vary geographically for example, can be adjusted in a similar way. For example, the total value of a good produced in a region of a country depends on both the amount and the price. To compare the output of different regions, the nominal output in a region can be adjusted by repricing the goods at common or average prices.