## Introduction

When expected inflation remains constant, changes in the nominal interest rate can have a significant impact on the real interest rate. The real interest rate is the nominal interest rate adjusted for inflation, and it reflects the true cost of borrowing or the return on investment. In this article, we will explore how the real interest rate is affected when the nominal interest rate falls in a scenario of constant expected inflation.

## The Relationship between Nominal and Real Interest Rates

To understand the impact of a falling nominal interest rate on the real interest rate, it is essential to grasp the relationship between these two rates. The nominal interest rate is the rate at which money grows over a specific period, without considering inflation. On the other hand, the real interest rate takes into account the effect of inflation on the purchasing power of money.

The formula to calculate the real interest rate is as follows:

**Real Interest Rate = Nominal Interest Rate – Expected Inflation Rate**

When expected inflation is constant, any change in the nominal interest rate will directly affect the real interest rate. If the nominal interest rate falls while expected inflation remains constant, the real interest rate will decrease as well.

## Impact of Falling Nominal Interest Rate on Real Interest Rate

A falling nominal interest rate means that the cost of borrowing or the return on investment decreases. This can have several implications for borrowers and lenders.

For borrowers, a lower nominal interest rate means that they can obtain loans at a lower cost. This encourages borrowing and can stimulate economic activity. However, when expected inflation is constant, the decrease in the nominal interest rate is offset by a corresponding decrease in the expected inflation rate. As a result, the real interest rate remains relatively stable, and borrowers do not experience a significant change in the true cost of borrowing.

On the other hand, for lenders or investors, a lower nominal interest rate implies a lower return on investment. While this may seem unfavorable, it is important to consider the effect of inflation. When expected inflation is constant, the decrease in the nominal interest rate is offset by a decrease in the expected inflation rate. As a result, the real return on investment remains relatively stable, and lenders or investors do not experience a significant change in the true return on investment.

## Factors Influencing Real Interest Rates

While the relationship between nominal and real interest rates is influenced by expected inflation, other factors can also impact the real interest rate. These factors include:

1. Economic growth: Higher economic growth can lead to higher real interest rates as demand for borrowing increases.

2. Central bank policies: Monetary policies implemented by central banks, such as changes in the money supply or interest rate targets, can influence real interest rates.

3. Market expectations: Market expectations of future inflation can affect the real interest rate. If market participants expect higher inflation in the future, the real interest rate may increase to compensate for the expected loss in purchasing power.

4. Risk premium: The risk associated with a particular investment or loan can influence the real interest rate. Higher-risk investments or loans may require a higher real interest rate to compensate for the additional risk.

## Conclusion

In summary, when expected inflation is constant, a decrease in the nominal interest rate will result in a decrease in the real interest rate. Borrowers can benefit from lower borrowing costs, while lenders or investors may experience a lower return on investment. However, it is important to consider other factors that can influence the real interest rate, such as economic growth, central bank policies, market expectations, and risk premiums.

## References

– Federal Reserve Bank of St. Louis: research.stlouisfed.org

– Investopedia: investopedia.com

– Bank for International Settlements: bis.org