Nominal vs. Real Interest Rates: Formulas and Key Differences

What Is Nominal Interest Rate?

Nominal interest rate refers to an interest rate that has not been adjusted for inflation. This contrasts with the real interest rate, which factors in the declining value of money.

Investors typically consider the real interest rate when looking for the most profitable places to invest their money. It is calculated by subtracting the inflation rate from the nominal interest rate.

Nominal can also refer to the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest.

Basics of Nominal Interest Rate

Central banks set short-term nominal interest rates, which form the basis for other interest rates charged by banks and financial institutions. Nominal interest rates may be held at artificially low levels after a major recession to stimulate economic activity through low real interest rates, which encourage consumers to take out loans and spend money. However, a necessary condition for such stimulus measures is that inflation should not be a present or near-term threat. In the U.S., the federal funds rate, set by the Federal Reserve, is an example of a nominal rate.

During times of inflation, central banks usually set high nominal rates. They might overestimate inflation and keep nominal rates too high. High interest rates can harm the economy by discouraging spending.

Nominal interest rates differ from real and effective interest rates. Real interest rates tend to be important to investors and lenders, while effective interest rates are significant for borrowers as well as investors and lenders.

Even though the nominal rate is stated for a loan, it's not usually what consumers pay. Consumers pay an effective rate, which changes due to fees and compounding. To that end, the annual percentage rate (APR) differs from the nominal rate, as it takes fees into account, and annual percentage yield (APY) takes both fees and compounding into account.

How to Calculate Nominal Interest Rate

 You can calculate the nominal interest rate (n) for a set period if you know the effective interest rate:

n = m × [ ( 1 + e)^1/m - 1 ]

Where:

• e = effective rate
• m = number of compounding periods

However, most borrowers typically want to know the effective rate, as the nominal rate is often the rate that is stated. The formula for effective interest rate (e) is:

e = (1 + n/m)^m - 1

Where:

• n = nominal rate
• m = number of compounding periods

For example, if a loan’s stated (nominal) rate is 8% and it’s compounded semiannually, then the effective interest rate (e) would be:

e = [1 + 0.08/2]² - 1 = 8.16%

Comparing Nominal and Real Interest Rates

Unlike the nominal rate, the real interest rate takes the inflation rate into account. The equation that links nominal and real interest rates can be approximated as nominal rate = real interest rate + inflation rate, or nominal rate - inflation rate = real interest rate.

To avoid purchasing power erosion through inflation, investors consider the real interest rate, rather than the nominal rate. One way to estimate the real rate of return in the U.S. is to observe the interest rates on Treasury Inflation-Protected Securities (TIPS). The difference between the yield on a Treasury bond and the yield on TIPS of the same maturity provides an estimate of inflation expectations in the economy.

For example, if the nominal interest rate offered on a three-year deposit is 4% and the inflation rate over this period is 3%, then the investor’s real rate of return is 1%. On the other hand, if the nominal interest rate is 2% in an environment of 3% annual inflation, the investor’s purchasing power erodes by 1% per year.