The Real Interest Rate: Nominal Rates Adjusted for Inflation

What this means

A savings account advertises a rate. A mortgage quotes a rate. A bond states a rate. Every one of those is a nominal interest rateThe stated or advertised interest rate, expressed in current dollars and not adjusted for inflation., and by itself it answers a narrower question than most people assume. It tells you how many more dollars you will have, or owe. It does not tell you what those dollars will buy.

That second question is the one that actually matters, and answering it requires subtracting inflationA sustained rise in the general price level, which reduces the quantity of goods and services a given amount of money can purchase.. The result is the real interest rateThe nominal interest rate minus the rate of inflation. It measures the change in purchasing power of an amount borrowed or saved., and the relationship is direct:

real interest rate = nominal interest rate minus the rate of inflation

Make it concrete with clean hypothetical numbers. Suppose you deposit 1,000 dollars at a nominal 3 percent. A year later you have 1,030 dollars, which is unambiguously more dollars. But suppose prices rose 3 percent over that same year. The basket of goods that cost 1,000 dollars now costs 1,030 dollars. Your real interest rate is 3 minus 3, which is zero. You gained thirty dollars and gained nothing at all. Your purchasing powerThe quantity of goods and services a given amount of money can actually buy. is exactly where it started.

Now push it further. Suppose inflation had instead been 5 percent while your account paid 3 percent. The real rate is 3 minus 5, which is negative 2 percent. You have more dollars and less stuff. This is not a paradox or an accounting trick. It is the ordinary condition of savings whenever inflation runs above the rates banks are paying, and it is why a negative real interest rateA real interest rate below zero, occurring when inflation exceeds the nominal interest rate, so purchasing power falls despite positive nominal earnings. is a genuine loss even though your statement shows a gain.

The same subtraction cuts the other way for borrowers, and the sign flips in whose favor it works. A borrower repays in dollars fixed by contract. If inflation runs high, those future dollars are easier to come by and buy less, so the borrower's real burden falls. High inflation quietly transfers value from lenders to borrowers, and the real interest rate is exactly the measure of how much.

One technical note worth having. Subtraction is an approximation of the exact relationship, which involves dividing rather than subtracting. At the modest rates typical of most economies, the approximation is close enough that economists use it routinely. At very high inflation rates the gap widens and the exact formula matters.

Why it matters

You will make two or three of the largest financial decisions of your life on the basis of interest rates: a student loan, a car loan, a mortgage. In every case the advertised number is nominal, and comparing nominal rates across different years is close to meaningless. A mortgage taken out at a high nominal rate during a high-inflation period may have carried a lower real cost than a mortgage at a much lower nominal rate taken out when inflation was near zero. Parents and grandparents who say "my first mortgage was at a rate you would not believe" are usually quoting the nominal number and leaving out the half of the story that would make it comparable.

The same correction applies to any claim about wages, prices, or returns over time. "Nominal" and "real" are the two most useful words in economics for detecting whether a comparison across years is honest.

Try it

1. Open FRED, the Federal Reserve Bank of St. Louis data site. Find the series for the 30-year fixed rate mortgage average in the United States. Set the range to the past 15 years and note the series ID you used.
2. In a second tab, find an inflation series. The Consumer Price Index for All Urban Consumers is the standard choice. Set FRED's units to "Percent Change from Year Ago" so you are reading an annual inflation rate rather than an index level.
3. Build a table with three columns: year, average nominal 30-year mortgage rate, and annual inflation rate. Fill in all 15 years. Record actual values from the site. Do not estimate from memory and do not use any figure quoted in this lesson.
4. Add a fourth column and compute the real mortgage rate for each year by subtracting inflation from the nominal mortgage rate. Label the column clearly as an estimate, since you are using the approximation.
5. Plot all three series, nominal rate, inflation, and real rate, on a single set of axes across your 15 years. Use a visibly distinct line for each and mark the zero line.
6. Identify the year with the highest nominal mortgage rate in your data and the year with the highest real mortgage rate. Note whether they are the same year. If they are not, explain in writing exactly why they diverged.
7. Find any year in your data where the real rate you computed came out near zero or below zero. Describe in plain language what that meant for someone holding a mortgage that year: what happened to the real burden of their monthly payment?
8. Write the borrower-versus-lender analysis. For your highest-inflation year and your lowest-inflation year, state who benefited and who was disadvantaged relative to what both parties expected when the loan was signed. Be specific about the direction of the transfer.
9. Close with an argument. Two homebuyers borrow in different years, one at a much higher nominal rate than the other. Using only your own table, construct a defensible case that the higher nominal rate was the better deal, and state the exact condition that has to hold for your case to work.

Check yourself