Real vs Nominal Interest Rates: What Inflation Takes Away

The nominal interest rate is the rate written on a loan or deposit. The real interest rate is what is left after inflation, and it shows how much buying power a saver gains or a borrower gives up. A 6 per cent deposit sounds good, but if prices rise 7 per cent over the same year, the saver can buy slightly less than before.

Two rates for the same money

The European Central Bank explains the nominal rate as the rate that is actually agreed and paid. A borrower pays it on a mortgage, and a saver receives it on a deposit. The real rate is the nominal rate adjusted for inflation. It tells you what happens to purchasing power, not just the number in an account.

The quick rule from the ECB's explainer is: real rate = nominal rate minus inflation.

A worked example

The ECB uses a euro example. A saver puts 1,000 euros in a deposit for a year at a nominal rate of 2.5 per cent, and ends with 1,025 euros. If prices rise 3 per cent in that year, goods that cost 1,000 euros a year earlier now cost 1,030 euros. The saver is 5 euros short of the same basket, and the real return is 2.5 minus 3, which is minus 0.5 per cent.

The same logic works for any currency. Put in your own numbers:

• Nominal rate: 6 per cent
• Inflation over the same year: 4 per cent
• Approximate real rate: 6 minus 4, which is 2 per cent

The Fisher equation

Economists link the three numbers with the Fisher equation, named after the economist Irving Fisher. Wikipedia gives its exact form as (1 + i) = (1 + r) x (1 + p), where i is the nominal rate, r is the real rate and p is inflation. Rearranged, the real rate is r = (i minus p) divided by (1 + p).

When rates and inflation are low, the simple subtraction is close enough: r is roughly i minus p. The two methods drift apart when numbers get large. Wikipedia's example is a lender who earns 10 per cent while prices rise 25 per cent. Subtraction suggests a loss of about 15 per cent, but the exact calculation, 1.10 divided by 1.25 minus 1, gives a loss of 12 per cent. The article itself calls the approximation a bit rough.

Exact versus approximate: a check

Take a nominal rate of 8 per cent and inflation of 5 per cent. Subtraction gives 3 per cent. The exact formula gives 1.08 divided by 1.05, minus 1, which is about 2.86 per cent. For everyday comparisons the gap is small, but it grows as inflation rises.

Before and after: ex-ante and ex-post

Inflation is only known once the year is over, which creates two versions of the real rate. Wikipedia describes them this way:

• Ex-ante real rate: the rate expected when the loan or deposit is made, using expected inflation. Different people can hold different expectations.
• Ex-post real rate: the rate known afterwards, using the inflation that actually happened.

A fixed-rate deposit has a known nominal return, but its real return is only certain in hindsight. The article notes that inflation-indexed bonds have made the market's expected real rates observable, because their payments are tied to measured inflation.

Why a positive rate can still lose value

The ECB points out that a positive nominal rate can still mean a loss in buying power when inflation is high. Its example is the early 1980s, when nominal rates in the euro area were high, but inflation was higher still, so the average real rate was low.

The reverse also holds for borrowers. When inflation is above the loan rate, the real rate is negative, and the amount repaid is worth less in goods than the amount borrowed.

Which inflation figure to use

The calculation depends on which price measure you choose. Most countries publish a consumer price index, and the headline figure is an average across a basket of goods. Your own spending may rise faster or slower than that average. If you want to know how the index is built, see our article on how inflation is measured.

Key points

• Nominal rate: the rate stated and paid.
• Real rate: the nominal rate adjusted for inflation.
• Quick estimate: subtract inflation from the nominal rate.
• Exact: divide (1 + nominal) by (1 + inflation) and subtract 1.
• Expected inflation gives an ex-ante rate; actual inflation gives an ex-post rate.

Sources

• Nominal and real interest rates, European Central Bank
• Real interest rate, Wikipedia