Inflation and Real Returns Explained

A 7 percent return sounds like a good year until you ask what it bought. If prices rose 2.5 percent over the same period, the money grew by 7 percent and each of those dollars bought slightly less than it did a year earlier.

The compound interest calculator reports both figures, because a projection that only shows the nominal number is describing a balance rather than describing what the balance is worth.

Two different numbers

Nominal is the rate on the account: 7 percent. It is the number on the statement, and it is what the balance in the account does.

Real is the rate after inflation: what the balance is actually worth in purchasing power. It is the number that describes whether the money gained or lost ground.

The two are not the same, and the relationship between them is the Fisher equation:

(1 + nominal) = (1 + real) × (1 + inflation)

Solving it for the real rate:

real = (1 + nominal) / (1 + inflation) − 1

At 7 percent nominal and 2.5 percent inflation, the real rate is 4.39 percent, not the 4.5 percent that simple subtraction gives. The difference is small at these rates and grows at higher ones, which is why the exact formula is worth using.

A worked example

The calculator’s real-value column does the same conversion on the balance rather than on the rate. A $10,000 balance at 7 percent with $500 a month over 10 years ends at $92,000-something in nominal terms. At 2.5 percent inflation, the same balance in the purchasing power of the starting year is around $72,000-something.

The nominal figure says the account holds $92,000. The real figure says it holds what $72,000 bought ten years ago. Both are true, and they answer different questions. The first is about the account. The second is about your life.

Which inflation number to use

The Bureau of Labor Statistics publishes the Consumer Price Index, which is the standard general-purpose measure of price change, together with the underlying data tables and a calculator for specific periods.

For a long horizon, the choice of index matters more than people expect, because the index that matches your own spending is the one that describes your own purchasing power. The headline CPI tracks a basket of goods and services bought by typical households, and it is the default for most calculations, including the one on this site.

Inflation and fixed debts

The relationship runs the other way for a fixed-rate mortgage. A payment that is fixed for thirty years gets smaller in real terms as prices rise. The borrower repays the loan with money that is worth less each year than the money they borrowed with.

This is the argument for paying down a fixed-rate loan early when real rates are high, and it is arithmetic rather than opinion. It is also why a fixed-rate loan is a fixed liability in nominal terms and a shrinking one in real terms.

Inflation and the figures in the tools

The compound interest calculator applies the inflation rate to the balance, producing the real-value column. The rent versus buy calculator does not adjust for inflation, because it compares two cash-flow series over a horizon and the inflation adjustment would apply to the rent series as well as to the ownership series; the tool leaves the choice of how to handle inflation outside the calculation and says so.

The mortgage calculator does not adjust for inflation either, for the same reason. A payment in thirty years is a fixed number of dollars, and what that number is worth is a question about the future rather than about the loan.

What a real return is not

A real return is a calculation on assumed numbers. The inflation rate used is historical, the nominal rate is assumed to be constant, and the contributions are assumed to be constant. Each of those assumptions is reasonable for a projection and false for the future, and the result should be read as “under these assumptions” rather than as a prediction.

The point of showing the real figure is not the prediction. It is that a number without it is incomplete.