Real interest rate: what a rate is worth after inflation

A rate of 12% a year sounds like a good return until prices rise 8% in the same year. What matters is how much more you can buy at the end, and that is what the real rate measures. This guide explains the difference between nominal and real rates, shows the formula that connects them and applies it to investments and to loans.

Nominal and real rates

The nominal rate is the one written in the offer or in the contract, and it is measured in money. The real rate is measured in purchasing power: it is what remains of the nominal rate once the rise in prices is taken out. A nominal return of 12% with inflation of 12% leaves you with the same purchasing power you started with, which is a real return of zero.

The formula

The nominal rate, the real rate and inflation are linked by (1 + nominal) = (1 + real) × (1 + inflation), so the real rate is (1 + nominal) ÷ (1 + inflation) − 1. Subtracting inflation from the nominal rate is a shortcut that only works when both are small. The higher they are, the bigger the error, and for a positive return the shortcut always overstates the result.

An example with numbers

In the first row the shortcut says 8.00% and the formula 7.69%. In the last row the return is negative either way, and it is the formula's -3.64% that tells you how much purchasing power was actually lost.

Tax changes the picture further. A product that yields 12% before tax, held for 12 months, leaves R$ 990.00 on R$ 10,000.00 after a 17.5% income tax, which is 9.90%. With inflation at 4%, the real return after tax is 5.67%, not the 7.69% of the first row. The tax is charged on the nominal yield, so inflation does not reduce what is taxed.

Loans and real rates

A loan at 1.8% a month costs 23.87% a year in nominal terms. With inflation at 4% a year, that is about 19.11% in real terms: the money you repay is worth less, in purchasing power, than the money you borrowed. That does not make the loan cheap. The benefit exists only if your income rises with prices, because the installment you pay is fixed in money. In loans whose rate follows an inflation index, such as the IPCA in Brazil, the inflation is added on top of a fixed rate, and what is agreed at signing is the real part.

Where to find inflation figures

Each country has an official index. In Brazil it is the IPCA, published by the IBGE. In the United States, the consumer price index (CPI), by the Bureau of Labor Statistics. In the euro area, the harmonised index of consumer prices (HICP), by Eurostat. Use the one for the country and currency of the money you are comparing, and remember that what you know is past inflation: the rate you lock in today will meet whatever inflation turns out to be.

Mistakes to avoid

• Reading a high nominal rate as a high real one. In a year of high inflation, a high nominal rate can be a small or even a negative real return.
• Comparing a nominal rate in one country with a real rate in another, or in a different currency.
• Forgetting the tax: it takes a share of the nominal yield, whatever inflation did.
• Assuming a return that does not beat inflation after tax is safe. It may be protected from losses in money, but it loses purchasing power.

How to use it with the tools

The investment comparison shows the net return after tax in nominal terms. To get the real return, apply the formula to that figure with the inflation you expect. For Brazil, the guide on CDI, Selic and IPCA explains the indexes. To decide between paying a debt and investing, see paying off a debt or investing, and for the bases a rate can come in, nominal and effective rates.