Nominal vs real return: which one to use

Nominal vs real return is the difference between counting dollars and counting what dollars buy. The nominal return is what a statement shows. The real return is what is left once prices have risen too. Both are correct answers to different questions, and the real return calculator converts one into the other for any rates you enter. The costly mistakes come from using one where the other belongs.

Nominal vs real rate of return: the two definitions

A nominal return measures growth in money. If $10,000 becomes $10,700 in a year, the nominal return is 7%, whatever happened to prices meanwhile.

A real return measures growth in buying power. If the things you buy cost 2% more by the end of that year, the $10,700 buys what about $10,490 bought at the start. The real return is 4.90%.

The second number is always smaller while prices are rising. It is not a pessimistic version of the first. It answers a different question.

Why 7% minus 2% is not 5%

Subtracting is the usual shortcut, and it is slightly wrong. Inflation eats into the balance after the year's growth, so the exact sum divides instead:

real return = (1 + nominal) ÷ (1 + inflation) − 1

At 7% and 2% that is 4.90%, not 5.00%. A tenth of a point looks like nothing, but it compounds like any other rate. $10,000 for 30 years at 5% grows to $43,219; at 4.90% it grows to $42,025. The shortcut flatters the result by $1,194, and it always errs in the same direction.

The gap widens as the rates rise. At 10% nominal and 5% inflation the real return is 4.76%, a quarter of a point below the 5% the subtraction gives. Fees come off before the division: 7% with a 0.5% fee and 2% inflation is 4.41% real.

A nominal projection is a figure in future dollars

This is where the difference is largest, and where it is easiest to miss. Put $10,000 in and add $500 a month for 30 years. If returns average 7%, the pot ends at $660,849, of which $190,000 was paid in.

That figure is real money in the sense that the account will show it. What it buys depends on prices:

• No inflation: $660,849 of today's buying power
• 2% inflation: $364,835
• 3% inflation: $272,261

Same pot, same return. At 3% inflation, the buying power is well under half the number on the statement. Nothing has gone wrong. Thirty years of rising prices is simply a large effect, and a projection quoted in future dollars leaves it out. The compound growth calculator shows both: set an inflation rate under its extra options and the result is restated in today's money alongside the nominal figure.

The one rule: match the rate to the target

Neither rate is the right one in general. Each is right for one kind of target:

• A target in future dollars (a balance on a statement, a loan to pay off in year 20) goes with the nominal rate.
• A target in today's money (an income that buys what $40,000 buys now, a pot worth what $1 million is worth now) goes with the real rate.

Mix them and the answer is wrong by the whole of inflation. Take a $1 million target over 30 years. At a 7% nominal return, $855 a month gets there. But if the $1 million was meant in today's money, the result falls well short: at 2% inflation, that future $1 million buys what $552,071 buys today.

Worked at the real rate instead, 4.90%, the monthly figure is $1,248. That figure is also in today's money, so it has to rise with prices each year to stay the same in real terms. Raised once a year by 2% and grown at 7%, it ends at about $1.79 million in future dollars, which is just under $1 million in today's money. The small shortfall comes from raising the payment once a year rather than continuously.

That last point is the subtle half of the rule. A real rate assumes everything else in the sum is in real terms too, including the contributions. A flat $500 a month grown at 4.90% gives $442,742. The same $500 raised each year with 2% inflation, grown at 7% and converted back to today's money, gives $438,505. Within about 1% of each other, because they describe the same plan. Use a real rate with contributions that never rise, and you have quietly assumed a saver who keeps raising them.

Real interest rates on savings

Cash makes the difference easiest to see, because the nominal rate is printed on the account. At a 4% savings rate and 3% inflation, the real rate is 0.97%. At 1% and 4% inflation, it is −2.88%.

That second case is the one people notice least. $10,000 left for ten years at 1% shows $11,046 on the statement. If prices rose 4% a year over the same decade, that balance buys what $7,462 bought at the start. The number went up every month while its buying power went down. The inflation calculator shows the same effect on any amount, in either direction.

Where a real rate is quoted directly

Most rates you see are nominal. US Treasury inflation-protected securities are an exception in how they work. According to TreasuryDirect, the principal of a TIPS is adjusted using a version of the Consumer Price Index, interest is paid on the adjusted principal, and at maturity the holder gets the inflation-adjusted principal or the original principal, whichever is greater. Because the principal already moves with prices, the fixed rate on a TIPS works as a rate above inflation rather than in plain dollars.

Not financial advice. Worked examples assume steady returns and steady inflation at the rates stated, contributions at the end of each month, and no tax. Real markets and real prices do not move in straight lines. The TIPS description summarises TreasuryDirect.