There is Taylor rule in economics that shows how to relate nominial interest rate with inflation and GDP.
$i_t = \pi_t + r_t^* + a_\pi ( \pi_t - \pi_t^* ) + a_y ( y_t - \bar y_t )$ In this equation, $\,i_t\,$ is the target short-term nominal interest rate (e.g. the federal funds rate in the US), $\,\pi_t\,$ is the rate of inflation as measured by the GDP deflator, $\pi^*_t$ is the desired rate of inflation, $r_t^*$ is the assumed equilibrium real interest rate, $\,y_t\,$ is the logarithm of real Gross Domestic Product, and $\bar y_t$ is the logarithm of potential output, as determined by a linear trend. In this equation, both a_{\pi} and a_y should be positive. (Wikipedia, Taylor Rule)
So, the question is, how did this equation come up mathematically?