Real vs Nominal Return: What Inflation Takes

0:00Same jar, same sign — and a price tag that climbs too ▶

Say a jar pays you 5%, a little every day — the same jar as last time. After a year it holds 5.13% more, and that feels like the whole story. It is not, because while the jar was filling, something else was climbing too: the price tag on the things you want to buy. What matters is not how much money is in the jar, but how much more it buys than a year ago. Say prices climb 3% in that same year — nothing dramatic. Now put the jar on the basket scale, which measures baskets instead of dollars. And the balloon settles at about 2%. The first number, the one on the jar, is the nominal return: the raw number, with nothing taken out. The second, what the shelf lets you buy, is the real return: the same jar, with inflation taken out. The statement says 5.13, the shelf says about 2, and the difference is what inflation quietly took. But about 2 is not a number you can plan with — so what is it, exactly? All you need is one idea: your money and the price tag are both climbing, and only the gap between them is real. Here is the whole idea on one pole.

1:26The basket scale: nominal is the dollar's climb, real is the gap ▶

Your dollar climbs the basket scale at the jar's rate. The price of a basket climbs the very same scale, at the shelf's rate. Watch them for one year: the dollar reaches 5.13, the price tag reaches 3. What you can buy is the gap between the two, and only the gap — that gap is the balloon. Before the exact number lands, guess: of the 5.13 the jar earned, did inflation take less than half, or more? That gap is the real return, and it has an exact formula — so where does that formula come from? Start with one basket, and say it costs one dollar today.

2:10How to compute it: real = (1 + n) ÷ (1 + p) − 1, from a basket ▶

Next year the price tag on that basket says a dollar and three cents. And your dollar in the jar has grown to a dollar and a little over five cents. So divide what you have by what one basket costs: a dollar and a little over five cents, by a dollar and three cents. That buys 2.06% more basket — and that is the real return, exactly. So of the 5.13, inflation took 3 and left you 2: more than half was never yours. Give the two climbers a letter each on the pole: the jar's rate, and the price rate. One plus the jar's rate, divided by one plus the price rate, minus one: that is the real return. Your money grew by one factor, and the price by another. Divide the two, and you get how many baskets you buy now for each basket you bought then. Take away that one old basket, and what is left is the real return. Subtracting instead, 5.13 minus 3, gets you close, 2.13, but that is a shortcut, not the formula. Irving Fisher wrote this relation down more than a century ago, and it still carries his name. His point was simple: a lender and a borrower both think in baskets, not in dollars — which is exactly why you divide.

3:39Exact: 2.0648% — what inflation takes each year ▶

So hold the two numbers side by side: the statement says 5.13, the shelf says about 2. The balloon settles on 2.06, and the exact number stands in gold. Losing about 3 points a year sounds like a rounding error — which is exactly why nobody notices it. Now leave the jar alone for thirty years, and touch nothing. After thirty years the statement shows $44,812 — the same jar as last time.

4:07Thirty years: $44,812 on the statement, $18,462 on the shelf ▶

But the basket has been climbing the same scale every single year, and it now costs more than twice as much. Put the jar back on the basket scale, and it buys what $18,462 buys today. The statement says one number, and the shelf says less than half of it. That is the number that quietly took most of it back: more than $26,000, never withdrawn, never charged. And if the price tag had climbed at 5% instead of 3? Then thirty years of 5.13 leave you with barely more than you put in. That is where it takes it all back. And the other jar from last time, the one that paid its 5% just once a year? It would buy exactly what it bought on day one, nothing more.

5:07The whole story ▶

So here is the story in one picture. Nominal is the number on the statement. Real is the number on the shelf, and only the gap between them is yours. One of them has inflation taken out, the other has not — and only the corrected one tells you whether you got richer. Same jar, same rate, and one price tag that never stops climbing — and that's the math behind the money.

5:34What's next: Time Value of Money ▶

Next time: what a dollar next year is worth today — and why nobody who says 3% means 3 cents. And for you: what inflation number do you plan with? Tell me in the comments below. I'm the MoneyMathician, and if you subscribe, the next one will find you. Until then: do the math!