Suppose that the nominal inflation rate is 4 percent and the inflation premium is 2 percent. What is the real interest rate? Alternatively, assume that the real interest rate is 1 percent and the nominal interest rate is 6 percent. What is the inflation premium?

The inflation premium helps the lenders to decide the nominal interest rate to keep the value of interest payment (or real income) from falling in the future due to price changes. Inflation premium is the expected rate of inflation after a certain time.

The following equation shows the relationship between nominal interest rate, real interest rate, and inflation premium:

Nominal Interest Rate = Real Interest Rate + Inflation Premium

Therefore, when the nominal interest rate is 4%, and the inflation premium is 2%, you have

$$\begin{gathered} \mathrm{Nominal}\mathrm{Interest}\mathrm{Rate}=\mathrm{Real}\mathrm{Interest}\mathrm{Rate}+\mathrm{Inflation}\mathrm{Premium} \\ 4=\mathrm{Real}\mathrm{Interest}\mathrm{Rate}+2 \\ \mathrm{Real}\mathrm{Interest}\mathrm{Rate}=4-2 \\ =2\% \end{gathered}$$

Therefore, the real interest rate is 2%.

When nominal interest rate is 6%, and real interest rate is 1%, the inflation premium is 5%, as calculated below:

$$\begin{gathered} \mathrm{Nominal}\mathrm{Interest}\mathrm{Rate}=\mathrm{Real}\mathrm{Interest}\mathrm{Rate}+\mathrm{Inflation}\mathrm{Premium} \\ 6=1+\mathrm{Inflation}\mathrm{Premium} \\ \mathrm{Real}\mathrm{Interest}\mathrm{Rate}=6-1 \\ =5\% \end{gathered}$$

Hence, the expected inflation rate is 5%.