Nominal vs Real Interest Rates

Nominal and Real Interest Rate Definition

The difference between nominal and real interest rates is an adjustment for inflation. Since inflation plays such a key role in so economic measures of value, economists came up with terms that describe things that do and do not account for inflation.

Specifically, economists call any value that is measured in absolute terms, or exactly as-is, a nominal value.

Conversely, economists call any value that has been adjusted for inflation a real value.

The reason is fairly intuitive. If you the price of a pack of gum was $1 one year ago and that same pack of gum costs $1.25 today, then your purchasing power has gone down. Specifically, inflation is 25% and your purchasing power has decreased by 25%. However, if instead you deposited that $1, and your bank paid 25% interest, then it has grown to $1.25 today, and what has happened to your purchasing power? It has stayed exactly the same!

The word "real" means we adjust for inflation so that we're measuring the true change in actual purchasing power, in terms of the market basket of goods and services.

For simplicity, we will discuss interest rates in terms of what someone would pay, or receive, for a loan.

Since lenders earn money by charging an interest rate and borrowers pay that interest rate, it's useful to consider both the nominal and real interest rates when considering borrowing or lending.

Nominal and Real Interest Rate Examples

Lenders receive interest payments as earnings, but the value of those expected future earnings depends on inflation. This is why lenders try to predict future inflation. Let's look at an example with and without predicting future inflation.

Suppose a lender gives you a one-year loan for $1,000 today at an interest rate of 3% without even considering potential inflation, and a year from now you pay the lender back $1,030, but inflation has increased all prices by 5%, then effectively the lender has actually lost money!

How did the lender lose money? They lost money because the $1,000 they lent you no longer buys what it did a year ago when they provided the loan. Indeed, even the $1,030 you repaid to them no longer buys the same amount as the $1,000 that they lent to you. Since inflation was 5%, that means $1,000 last year has the same purchasing power as $1,050 today.

The real interest rate is the nominal interest rate minus inflation, so in this scenario the lenders' profit, which is the real interest rate they received, was -2%. They lost money. Imagine going into the lending business expecting to become rich and then ending up losing money!

Having learned their lesson, the lender does some research and discovers that smart economists like you have forecasted an inflation rate of 4% for the upcoming year. The lender decides to get back into the lending business, but this time they want to make sure they earn a 3% real return. They want to have 3% more purchasing power!

$RealInterestRate=NominalInterestRate-InflationRate$

In order to ensure a 3% profit as a real return, the lender charges a nominal interest rate equal to the sum of the desired real interest rate and the forecasted inflation rate. This time they offer the same $1,000 loan but now they charge a nominal interest rate of 7%, which is the sum of the 3% anticipated real return and the 4% anticipated inflation.

This is precisely how nominal interest rates, expected inflation, and real interest rates are connected.

Nominal and Real Interest Rate Differences

Let's now consider the market for money. The money market establishes the equilibrium interest rate where the demand for money and the supply of money intersect.

The market for money is depicted visually in Figure 1 below.

Fig 1. - Money market

Now, which interest rate do you think the money market refers to in Figure 1?

As it turns out, the money market responds to the nominal interest rate, which then influences the value of other financial assets.

You're probably wondering why, since the nominal interest rate doesn't inform lenders about their expected real returns.

The reason why the money market uses the nominal interest rate is that, by definition, the nominal interest rate includes the rate of inflation. Put another way, the opportunity cost of holding cash does and should include the real return that could be earned by depositing cash, and at the same time the erosion of purchasing power due to inflation.

Lenders start from the real return they want to receive and set their own nominal interest rates. They add together their expected real rate of return with their expectation of the inflation rate, and this is how they arrive at the nominal interest rate they charge on the money they lend.

Nominal and Real Interest Rate Similarities

How would the interaction between nominal and real interest rates be accounted for when different countries are involved? This is an interesting and important question because inflation rates in one country may be radically different than that of another country.

In this scenario, it would be most appropriate to use the Loanable Funds Market in an open economy.

Figure 2 shows the loanable funds market in an open economy.

Fig 2. - Loanable funds market in an open economy

In the loanable funds market, demand for loanable funds slopes downward because the lower the interest rate is, the more attractive taking out a borrowing is. Conversely, the supply for loanable funds slopes upwards because the higher the interest rate, the more lucrative it is to lend money.

What interest rate do you suppose they use in this market? Real or nominal?

Since exchanges on the loanable funds market can't account for actual future inflation rates, especially in another country, it relies on the nominal interest rate to illustrate equilibrium as demonstrated in Figure 2 above. However, since lenders and borrowers in this market actually only really care about the true or real interest rate associated with lending and borrowing, the Loanable Funds Market builds in expected inflation rates in each country.

For example, assume the equilibrium interest rate in Figure 2 is 5%, and assume furthermore that the future inflation rate in this country is suddenly expected to be 3% higher. Since the loanable funds market will take this into account, this expectation will result in a rightward shift in demand (an increase in demand) since borrowers are now willing to borrow at a nominal interest rate of 8% (Nominal Interest Rate = Inflation + Real Interest Rate).

Similarly, the supply curve of loanable funds will shift leftward (upward) so that lenders can be sure to receive a real interest rate of 5% (Real Interest Rate = Nominal Interest Rate - Inflation), or in other words a nominal interest rate of 8%. As a result of these forces, the new equilibrium exchange rate will be 8%. This phenomenon actually has a name. It's called the Fisher effect.

The Fischer effect is illustrated in Figure 3 below.

Fig 3. The Fischer effect

Nominal and Real Interest Rate Formula

The real interest rate formula is:

$RealInterestRate=NominalInterestRate-Inflation$

By extension, therefore, it's also true that the nominal interest rate formula is:

Now, according to the Fischer effect, in the loanable funds market, an increase in expected future inflation drives up the nominal interest rate by the amount of expected inflation.

But what if the expected inflation rate was negative? In other words, if people expected prices would drop at a deflation rate of, say 5%, would that mean that the nominal interest rate could potentially be negative according to the Fischer effect?

The answer is, obviously no. No one would be willing to lend money at a negative interest rate because they would simply do better by just holding cash, or investing in international markets. This simple concept captures what economists call the zero bound effect. In short, the zero bound effect simply states that the nominal interest rate cannot go below zero.

Is this the end of the story? Well, as you might have guessed, the answer is also no. You see, the zero bound on nominal interest rates can have a dampening, or limiting effect on monetary policy.

Assume, for example, that the central bank believes that the economy is underperforming, with output lower than potential output, and unemployment above the natural rate. The central bank would use the tools at its disposal to stimulate the economy positively by activating monetary policy to lower interest rates and increase aggregate demand.

However, if it happens that the nominal interest was already zero (or very low), the central bank could not push interest rates down below that to a negative rate. The central bank's power is limited in this situation. Banks will not lend additional money to consumers at a negative nominal interest rate, and firms would not spend any investment money because at a 0% interest rate, and a negative expected inflation rate, holding cash will have the best rate of return.

This is one of the reasons why central banks have to be very careful how far they go to positively stimulate their economies since they do not want to find themselves in this position.