Subtracting inflation from every number you just calculated

A balance of 10,000 grows at 6% a year for thirty years and ends at about 57,400. Over the same thirty years prices also rise at 6% a year.

The final balance buys exactly what 10,000 bought on the first day. Not approximately — exactly. Every number in the previous two lessons was this kind of number, and this lesson is the subtraction that has been quietly outstanding since then.

It is a division, not a subtraction

Most people take the real return by subtracting inflation from the nominal rate. Six minus three is three. That is close enough to be useful and wrong enough to matter at the top end.

The balance is multiplied by (1 + nominal) each year. Prices are multiplied by (1 + inflation) each year. What you can buy is the first divided by the second, so the real rate is:

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

At 6% and 3% that gives 2.913%, not 3%. At 6% and 3% nobody cares. At 30% and 25% the shortcut says five points and the division says four, and over a decade those are different worlds.

Predict

A balance grows 6% a year while prices rise 3% a year. What is the real return?

Choose one answer

Exactly 3%A little under 3%A little over 3%It cannot be worked out without knowing the balance

Lock in answer

Watch the two lines separate

Two controls move: the nominal return and inflation. The chart draws the balance as printed, and the same balance measured in the prices of the first day.

Real versus nominal

≈ Hypothetical model, not a forecast

Separates the headline growth of a balance from what it can actually buy once prices have moved.

It assumes

• Inflation runs at exactly the same rate in every one of the thirty years.
• The nominal return is also identical in every year.
• Purchasing power is measured against the prices of the starting day.
• One single basket of prices stands in for everything anyone buys.

It ignores

• That any real basket of prices moves unevenly, item by item
• Tax, which is charged on nominal gains rather than real ones
• Currency effects and anything bought from abroad

Find a pair of settings where the balance more than triples over the thirty years and buys nothing more at the end than it did at the start.

Nominal return6%

The number printed on the statement, before inflation is taken off.

Inflation3%

Real return

2.913%

Final balance, nominal

57,435

Final balance, in starting prices

23,662

Price level

2.43

What one unit of the final balance buys

0.412

• Balance as printed
• Balance in starting prices

◷ Not there yet — keep moving the controls.

Whenever the two rates match, the lower line is perfectly flat regardless of how steep the upper one is. A balance can grow by a factor of six, or sixty, and still be standing precisely still.

Check

Two savers, thirty years each. One earns 8% nominal with 6% inflation. The other earns 3% nominal with 1% inflation. Which ends with more purchasing power?

Choose one answer

The first, by a wide margin — 8% is far more than 3%The second, narrowlyThey are identical, because both are two points above inflationThe first, because inflation also inflates the contributions

Check answer

›The asymmetry tax quietly introducesOptional

Tax, where it applies to investment growth, is generally charged on the nominal gain rather than the real one.

Take a balance that grows 6% while prices rise 6%. The real gain is zero. The nominal gain is 6%, and a tax charged on that is a tax on a gain that did not happen, paid out of capital. In high-inflation periods this can produce a positive tax bill on a position that lost purchasing power all year.

That is a mechanism, and it travels. The rates, the thresholds and whether it applies at all do not.

Worth remembering

• Nominal is the number on the statement; real is what that number buys.
• The real rate is (1 plus nominal) divided by (1 plus inflation), minus one — a division, not a subtraction.
• Roughly: 6% nominal with 3% inflation is a real return of about 2.9%, and the shortcut overstates it.
• When the nominal return equals inflation, purchasing power is exactly flat however large the balance grows.
• Two very different nominal rates can deliver nearly identical real outcomes, so a rate quoted without an inflation figure says little.