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What a Dollar Buys

When prices rise, each dollar buys a little less. An account earning interest can still lose ground if prices rise faster. Choose an interest rate and an inflation rate, and see the real return: how fast your buying power actually grows.

Economics Lesson 6.5 · Series 65 Lesson 2.5 · Personal Finance Lessons 7.1 and 10.1 · about 15 minutes

Click or tap the chart to read any year. With the chart focused, the left and right arrow keys move one year (Home and End jump to the ends).

Real return (exact)per year
Quick estimate: rate − inflation
Prices double in
Dollars in the account
What they buy, in today’s dollars
Same cash in a drawer, in today’s dollars

What a dollar buys

The same thing in a spreadsheet

Your numbers

Use any rates you like: these are your own what-if numbers, not a forecast or a record of past years.

$
%
%

Both rates are yearly and compound once a year.

Try a what-if

Nominal and real

The nominal rate is the one the bank quotes: how fast the number of dollars grows. Inflation is how fast prices rise. The real rate is how fast what you can buy grows. If your dollars grow by the factor 1 + n in a year while prices grow by 1 + i, your buying power grows by their ratio:

1 + r = (1 + n) / (1 + i), so r = (1 + n) / (1 + i) − 1.

This is the Fisher equation, named for the economist Irving Fisher. With 5% interest and 3% inflation, r = 1.05/1.03 − 1 ≈ 1.94%, not quite 2%.

The quick estimate

Most people simply subtract: r ≈ n − i. The estimate is too big by exactly (n − i)i / (1 + i), which is tiny when the rates are small and grows when they are large. Try the last what-if: at 30% interest and 25% inflation, subtracting says 5% but the truth is 4%.

Money in a drawer

Cash earns nothing, so its real return is 1/(1 + i) − 1: it loses buying power every year prices rise. After t years a dollar buys what 1/(1 + i)t dollars buy today. The rule of 72 works here too: divide 72 by the inflation rate to estimate how long prices take to double, and so how long a dollar takes to lose half its buying power.

This page leaves out taxes. Tax is charged on the nominal interest, so the real return after tax is lower still.

Check yourself

  1. A savings account pays 7% and prices rise 4% a year. Find the exact real return and the quick estimate.
    Answer

    Exact: 1.07/1.04 − 1 ≈ 2.885%. Estimate: 7 − 4 = 3%. The estimate is about 0.115 percentage points too high.

  2. You keep $1,000 in cash for 10 years while prices rise 3% a year. What will it buy, in today’s dollars?
    Answer

    1,000 / 1.0310 ≈ $744.09. In a spreadsheet: =PV(3%, 10, 0, −1000).

  3. Interest is 4% and inflation is 4%. What happens to buying power?
    Answer

    The real return is 1.04/1.04 − 1 = 0. The number of dollars grows, but they buy exactly what the starting amount buys today: you are running in place.

  4. At 30% interest and 25% inflation, how far off is the quick estimate?
    Answer

    Exact: 1.30/1.25 − 1 = 4%. The estimate says 5%, a whole point (a quarter) too high. Subtracting only works well when both rates are small.

The rates on this page are the ones you choose. Real inflation changes from year to year, and no one knows future rates in advance; the point is the arithmetic, which is the same for any numbers.

“Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt.” — Matthew 6:19