Nominal Interest, Real Interest, and the Fisher Equation: Videos & Practice Problems

The nominal interest rate is the stated or advertised rate on loans or deposits, not adjusted for inflation. It represents the percentage increase in money you receive or pay. The real interest rate, however, adjusts the nominal rate to account for inflation, reflecting the true increase in purchasing power. For example, if a bank offers a 5% nominal interest rate but inflation is 2%, the real interest rate is approximately 3%. This means your money's purchasing power grows by 3%, not 5%. The relationship is given by the Fisher equation: $r\approx i-\pi$, where $r$ is the real interest rate, $i$ is the nominal interest rate, and $\pi$ is the inflation rate.

Inflation reduces the purchasing power of money over time because prices of goods and services increase. Even if your savings earn interest, if the inflation rate is high, the real value of your savings might not grow as much as the nominal interest suggests. For example, if you save \$2,000 with a 5% nominal interest rate but inflation is 2%, the price of goods you want to buy also increases by 2%. This means you can buy fewer goods than if there were no inflation. The real interest rate, which accounts for inflation, shows the actual increase in purchasing power. Using the Fisher equation, the real interest rate is approximately nominal interest rate minus inflation rate, so in this case, 5% - 2% = 3%. Thus, your purchasing power grows by about 3%, not 5%.

The Fisher equation is a formula that relates nominal interest rates, real interest rates, and inflation. It is used to approximate the real interest rate by subtracting the inflation rate from the nominal interest rate. The equation is: $r\approx i-\pi$, where $r$ is the real interest rate, $i$ is the nominal interest rate, and $\pi$ is the inflation rate. This approximation works well when inflation rates are low. For example, if the nominal interest rate is 5% and inflation is 2%, the real interest rate is approximately 3%. This helps investors and savers understand the true growth of their money in terms of purchasing power.

Real interest rates can be negative when the inflation rate exceeds the nominal interest rate. This means that even though you earn interest on your savings, the purchasing power of your money decreases because prices rise faster than your returns. For example, if the nominal interest rate is 1% but inflation is 3%, the real interest rate is approximately -2%. Negative real interest rates imply that savers lose purchasing power over time if they keep money in low-interest accounts. This situation often occurs during periods of high inflation or economic stimulus when central banks keep nominal rates low.

Inflation is calculated by measuring the percentage change in the Consumer Price Index (CPI) from one year to the next. The CPI tracks the average price of a basket of goods and services over time. The formula for inflation is: $\frac{\mathrm{CPI}\_\mathrm{current}-\mathrm{CPI}\_\mathrm{previous}}{\mathrm{CPI}}\times 100$. This gives the inflation rate as a percentage, indicating how much prices have increased compared to the previous year. For example, if the CPI was 200 last year and 204 this year, inflation is ((204 - 200) / 200) × 100 = 2%.

During the 2008-2009 recession, the U.S. experienced a unique situation where the real interest rate was higher than the nominal interest rate. This occurred because of deflation, a period when prices decreased, resulting in a negative inflation rate. With nominal interest rates near zero, the real interest rate became positive as it was calculated by subtracting a negative inflation rate (deflation) from the nominal rate. This meant that the purchasing power of money increased over time despite low nominal returns. Such a scenario is rare and indicates that holding money was beneficial in terms of purchasing power during that recession.