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Inflation

What Is the Difference Between Nominal and Real? the number printed and the number that counts

In this chapter
  1. Every sum of money has two numbers
  2. The arithmetic, and it is one line
  3. Where you meet each one
  4. Nobody is required to show you the real number
  5. What follows from the distinction
  6. The test to apply
  7. The short version

Every sum of money has two numbers

One is the figure printed on the statement. The other is what that figure buys.

Nominal is the number as stated: your balance, your salary, your interest rate, the price on the tag. Real is the same number after adjusting for what prices did over the period.

They agree only when prices hold still, which they rarely do. The rest of the time, one of these numbers describes your money and the other describes your position.

The arithmetic, and it is one line

Take a savings account holding $10,000 that pays 0.5% a year, over ten years, while prices rise 3% a year.2

nominal balance after 10 years $10,511 price level after 10 years 1.34x real balance, in today's money $7,822

The account never lost money. Every statement showed a larger number than the one before. The holder is about 22% poorer in what that balance buys.

The quick version is subtraction: real is roughly nominal minus inflation. Earn 0.5% while prices rise 3%, and the real return is about −2.5% a year. For a precise figure, divide rather than subtract:

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

At 0.5% and 3%, that gives −2.43%. Subtraction is close enough for most decisions and gets you the sign, which is the part that matters.

Where you meet each one

Almost everything quoted to a household is nominal.

Quoted to you asNominalReal
Savings interestAPY on the accountnever quoted
Your salarythe offer letternever quoted
A pension or annuity paymentthe monthly figurenever quoted
Social Securitythe benefit, adjusted yearly by COLAthe COLA is the attempt
Home pricewhat it sold fornever quoted
Investment returnthe percentage in the appoccasionally, in fund literature
Treasury inflation-protected securitiesthe yield is quoted as real

The last row is the exception that shows the rule. TIPS and I Bonds are built so that the inflation part is handled separately, so their yields are stated in real terms.1 Everywhere else, the household is handed the nominal figure and left to do the adjustment, or to skip it.

Nobody is required to show you the real number

APY is a required disclosure. Lenders must state an APR. There is no equivalent requirement anywhere for real return.

That asymmetry is not an accident of formatting. The nominal number on a savings account is always the flattering one when inflation is positive, which it usually is. A bank quoting 0.4% is quoting the larger of the two numbers it could quote.

This is the shape of a fleece as Money Words, Defined: the 370 terms that decide what you pay defines it: a cost that is disproportionate, avoidable, and concealed by which figure gets disclosed rather than by any false statement. Nothing in the disclosure is untrue. The number that would change the decision is the one left out.

What follows from the distinction

A raise below inflation is a pay cut. The number went up and the position went down.

A fixed payment shrinks every year it stays fixed. A pension of $2,000 a month that never changes buys about half as much after 24 years at 3%.

Fixed-rate debt gets cheaper to service. The same logic that erodes a fixed payment you receive also erodes a fixed payment you make.

A house that doubled may barely have moved. Twenty years of 3% inflation multiplies prices by 1.81 on its own.

The test to apply

When you are given a number about money over time, ask two questions.

Is this nominal or real? If nobody says, assume nominal. That is the default in nearly every consumer disclosure.

Over what period, and what did prices do in it? A number without a period cannot be adjusted, and a period without an inflation figure leaves the adjustment undone.

For prices themselves, the rule of 72 works: divide 72 by the inflation rate to get the years until prices double. At 3%, prices double in 24 years. At 2%, 36 years. At 6%, 12 years.

The short version

Nominal is the figure as printed. Real is the figure after inflation. Real is roughly nominal minus inflation, and exactly (1 + nominal) ÷ (1 + inflation) − 1. Consumer disclosure quotes nominal almost everywhere — APY, salary, pension payment, house price — and requires the real figure nowhere. $10,000 earning 0.5% for ten years while prices rise 3% grows to $10,511 and buys what $7,822 buys today. The balance rose and the position fell, and only one of those two facts appears on the statement.

Also in these situations
  1. InflationThe printed number and what it buys, and the one line of arithmetic between them.
Sources
  1. Treasury inflation-protected securities adjust principal with the consumer price index, so their quoted yield is a real yield. Series I savings bonds carry a composite rate combining a fixed rate with an inflation component. Both are Treasury products whose terms are published by the Treasury.
  2. Savings account yields and inflation rates both move. The 0.5% and 3% used here are round figures chosen to make the arithmetic legible, not current readings. Check both before applying the result to a decision. ---

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