Real Rate Of Return Calculator

The year your investment went up and you got poorer

Your fund returned 5 percent. The statement says so, the number is not in dispute, and you are worse off than you were twelve months ago.

That happens whenever prices rose faster than 5 percent, and it happens more often than anybody enjoys admitting. Nothing was stolen, no fee was charged, and yet the money buys less than the smaller amount did a year earlier.

The real rate of return is the number that catches this. It takes what your investment did and asks the only question that finally matters: can you buy more than you could before?

Two inputs, one answer, and the answer is frequently smaller and occasionally negative.

Why this one divides instead of subtracting

Real rate of return = [ (1 + nominal) / (1 + inflation) - 1 ] × 100

Most people, asked to adjust a return for inflation, subtract. Ten percent return, six percent inflation, four percent real, done.

That is close and it is not right, and the reason is worth understanding because it applies to every inflation adjustment you will ever make.

Think about what actually happened over the year. You started with 100 and ended with 110. Meanwhile the thing you wanted to buy went from costing 100 to costing 106. So the real question is how many of that thing you can now buy: 110 divided by 106, which is 1.0377. You are 3.77 percent better off, not 4.

That is what dividing does. It compares your money against prices rather than deducting one percentage from another, and it is exact rather than approximate.

The missing 0.23 has a name, the cross term, and it exists because inflation erodes your gains as well as your original stake. Subtraction never notices that second erosion, which is why it always flatters you a little.

Our real interest rate calculator uses the subtraction form, which is the standard macroeconomics teaching version and perfectly serviceable at low rates. Run the same pair of numbers through both and the gap is visible: at 8 percent and 5 percent it is 3.000 against 2.857, and at 25 percent and 20 percent it widens to 5.000 against 4.167.

The rule of thumb: below about 5 percent inflation, either is fine. Above that, division, and this is the tool.

Tax first, then inflation, and never the other way round

Now the part that costs people real money, and that almost no calculator mentions.

Most investment returns are taxed. So a full picture needs two adjustments, one for tax and one for inflation. The obvious question is which order to apply them, and the obvious answer is that it should not matter.

It matters enormously, and there is only one correct order.

Tax comes first, because tax authorities levy on nominal gains. No tax system asks what inflation did before calculating what you owe. You are taxed on the money you appear to have made, whether or not you gained any purchasing power.

So the sequence is: take your nominal return, remove the tax, then deflate what is left.

Watch what happens if you do it the other way.

A 10 percent return, 30 percent tax, 6 percent inflation. Done properly it is 0.94 percent. Done backwards it is 2.64 percent.

One and seven tenths of a percentage point apart, and the wrong order is the flattering one, which is presumably why it survives.

The reason the gap is so wide is that the tax bill in the correct sequence is calculated on the full 10 percent, including the 6 percent that was pure inflation. You paid tax on a gain that only existed because prices moved. In the wrong sequence you are effectively taxed only on the real gain, which is not what happens in any tax system I am aware of.

To use this calculator that way, work out your after tax return by hand first, then enter that as the nominal figure. A 10 percent return taxed at 30 percent is 7 percent, and 7 is what goes in the first box.

What you need just to stand still

Turn that around and it produces something genuinely useful: the return required simply to preserve what you have, after both tax and inflation.

Breakeven nominal return = Inflation / (1 - tax rate)

Read the third row. At 6 percent inflation and a 30 percent tax rate, an investment returning 8.57 percent leaves you exactly where you started. Not ahead. Level.

Which reframes a great many savings products. A deposit paying 7 percent in that environment is a slow, taxed, invisible loss, and the statement will show a rising balance the entire time.

It also explains why tax sheltered accounts matter so much more in high inflation. Remove the tax and the breakeven drops straight back to the inflation rate, which in that example is nearly two and a half percentage points of headroom handed to you for nothing.

Whose inflation, exactly

The second box wants a single number for inflation. There is no single number, and which one you choose moves the answer.

Published inflation is an average of price changes across a basket of goods, weighted by how a typical household spends. Two things follow.

You are not the typical household. If a large share of your money goes on rent, school fees, healthcare and fuel, and those are rising faster than the index, your personal inflation rate is higher than the published one and your real return is worse than this calculator reports.

The reverse holds too. Somebody who owns their home outright, with a stable lifestyle and no education costs, may be experiencing meaningfully less inflation than the headline figure.

Different indices measure different things. A consumer price index tracks what households buy. A GDP deflator covers everything an economy produces, including capital goods, government spending and exports, and excludes imports. They can move apart, and over long stretches in the United States the GDP deflator has risen at a systematically lower rate than the consumer index. Our real GDP calculator uses the deflator, and it is the right measure for economic output and the wrong one for your grocery bill.

For personal returns, use the consumer price index for the country whose currency you actually spend. Which sounds obvious until you are holding a foreign currency investment, in which case the inflation that matters is the one where you will eventually spend the money, not where the asset happens to be listed.

And match the periods. An annual inflation figure against a return earned over eighteen months gives you a number that means nothing in particular.

Where this belongs in a decision

Three places, in ascending order of how much difference it makes.

Judging what happened. The obvious one. Take last year's return, deflate it, and find out whether you actually gained.

Comparing across periods. This is where nominal figures become genuinely misleading. A 12 percent return in a high inflation decade and a 6 percent return in a low inflation one are not what they appear, and only the real figures are comparable. Any historical performance claim quoted in nominal terms deserves this treatment before you believe it.

Planning anything long. The most important use, and the one people skip. Retirement projections, education funds, anything measured in decades. A plan built on nominal growth looks comfortable and a plan built on real growth looks alarming, and the alarming one is correct. Our ROI calculator will annualise a multi year return, and this tool then tells you what that annualised figure was actually worth.

Two things the number cannot see, worth keeping in view. It says nothing about risk, so two investments with identical real returns can have carried entirely different chances of losing everything. And it assumes you held throughout, so money added or withdrawn along the way needs a different treatment.

Hope this makes your statement a little easier to read honestly. If a figure here does not match what you have worked out yourself, do tell us, because we would much rather correct it than have you trusting the wrong number.

Questions people ask

Why not just subtract inflation from my return?

Because subtraction ignores that inflation erodes your gains as well as your original stake. It always overstates the real return slightly. At low rates the difference is trivial, at high rates it is not.

Where does tax fit in?

Before inflation, always, because tax is levied on nominal gains. Work out your after tax return first and enter that as the nominal figure. Doing it the other way round overstates the answer, by 1.7 percentage points in the worked example above.

Can the answer be negative?

Yes, whenever inflation exceeds your return. It means your money grew and your purchasing power shrank, which is a real and common outcome on cash deposits.

Which inflation figure should I use?

The consumer price index for the country where you will spend the money. If your own spending is concentrated in categories rising faster than the index, your real return is worse than the published figure suggests.

How does this differ from your real interest rate calculator?

Only in the formula. That one subtracts, this one divides. Division is exact. Subtraction is the standard approximation and is fine when both rates are small.

How much do I need to earn just to break even?

Inflation divided by one minus your tax rate. At 6 percent inflation and 30 percent tax that is 8.57 percent nominal, which buys you precisely nothing.

My return covers several years, not one.

Annualise it first, then deflate by the average annual inflation over the same period. Our ROI calculator handles the annualising step.

References

A note on the sources. The exact form of the inflation adjustment used here follows from the compounding relationship defined by the Securities and Exchange Commission's investor education office, and their free calculator can be used to check any figure on this page by compounding a real return forward. The point in the inflation section, that a consumer price index and a GDP deflator measure genuinely different things and have diverged systematically over long periods, is documented by the Bureau of Labor Statistics in its own comparison of the two, which is the reason this page is specific about which index to use.

1. U.S. Bureau of Labor Statistics, Comparing the Consumer Price Index with the gross domestic product price index and gross domestic product implicit price deflator, Monthly Labor Review, on the differing scope of the two measures and the systematically lower rate of increase in the GDP deflator over time. https://www.bls.gov/opub/mlr/2016/article/comparing-the-cpi-with-the-gdp-price-index-and-gdp-implicit-price-deflator.htm
2. U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Compound Interest, Investor.gov glossary. https://www.investor.gov/introduction-investing/investing-basics/glossary/compound-interest
3. U.S. Securities and Exchange Commission, Compound Interest Calculator, Investor.gov, useful for compounding a real return forward as an independent check. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
4. Federal Reserve Bank of St. Louis, FRED Economic Data, consumer price index and inflation series used to source the inflation input. https://fred.stlouisfed.org/