# What's the difference between real and nominal interest rates?

We all talk -- and often worry -- about interest rates. But as with most things involving money, what we mean by "interest rates" can vary considerably. For instance, economists distinguish between the "nominal" interest rate and the "real" interest rate, with the latter divided further between the "ex-ante" real interest rate and the "ex-post" real interest rate.

The nominal rate is the one people are most familiar with. When you go to bank, mortgage dealer or another source of loans, the rate they quote is the nominal rate.

However, the nominal interest rate isn't what people should care about when evaluating the rate they're paying on a loan. What matters is the inflation-adjusted interest rate, or real interest rate.

For example, say the price of an apple is $1. When someone loans $100, they are in effect loaning 100 apples. Now suppose the lender wants to get a "real" return of 10 percent on a loan of $100 for one year -- in other words, the lender wants to be able to buy 110 apples with the loan's proceeds. Also suppose the lender expects inflation to be zero, and he charges a 10 percent interest rate on the loan. Then the $110 the lender receives when the loan is repaid ought to be able to purchase 110 apples because the price of apples isn't expected to rise.

But what if the inflation rate turns out to be 10 percent, the same as the interest rate charged on the loan, rather than zero? Then during the year, the price of an apple increases from $1 to $1.10. When the loan is paid off and the lender receives $110, he'll be able to buy only 100 apples, not the 110 as desired when he made the loan. In this case, the "real" return is zero instead of the expected 10 percent.

The relationship that captures this is called the Fisher equation, which states:** **Nominal interest rate = real interest rate + rate of inflation.

When the loan is made, what the actual inflation rate will be is unknown, so the expected rate of inflation over the loan's period is used in the formula. Thus, in the example above, since the lender expects inflation to be zero, the nominal rate = the real rate = 10 percent. This is called the "ex-ante" real interest rate because it's calculated before the actual inflation rate is known.

Only after the loan is repaid, and the inflation rate for the loan's period is known, can we calculate the actual real return (meaning the "ex-post" real return on the loan. Using the formula above, the ex-post real rate in the example = the nominal rate - the actual inflation rate, or in this case 10 percent - 10 percent = 0 percent.

So, although the ex-ante, or expected real return, was 10 percent, the ex-post, or actual real return, was 0 percent.

The most important of these interest rates for financial decisions is the ex-ante real rate. The nominal rate doesn't tell the borrower and lender what the actual return will be in terms of purchasing power, and the ex-ante real rate is unknown at the time the decision to make/take the loan is made.

Unfortunately for researchers, this is the hardest of the three interest rates to calculate because it's difficult to know the expected inflation rates that borrowers and lenders use when making decisions on loans. Surveys such as the Survey of Professional Forecasters ask about inflation expectations, and inflation expectations can also be derived by looking at the difference in price between Treasury bills that adjust for inflation (known as TIPS) and those that do not. Expectations can also be estimated from econometric forecasts of inflation.

But all of these approaches have problems, so researchers can never be sure about the accuracy of their ex-ante real rate calculations.

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