Macroeconomics / purchasing power

Inflation and purchasing power

Convert nominal amounts into real purchasing power, and work out the nominal return you need just to stand still after inflation and tax. The Fisher relation is applied exactly rather than as a subtraction.

Inflation3.10%Real return after tax0.78%Cost of waiting$17,851

Real value after horizon

$36,845

Today’s $50,000 in 10.0 years

Purchasing power lost

26.3%

$13,155 of value eroded

Real return on investment

1.84%

5.00% nominal, after inflation

Nominal needed to beat tax

3.97%

To break even after 22% tax

Purchasing power by year

What today’s money is worth in real terms as prices rise, plus the nominal amount needed to keep pace.

3.10% inflation

Purchasing power by year
Year	Real value of today’s amount	Nominal needed to match	Loss
Year 0	$50,000	$50,000	-$0.00
Year 2	$47,038	$53,148	-$2,962
Year 4	$44,252	$56,494	-$5,748
Year 6	$41,631	$60,051	-$8,369
Year 8	$39,165	$63,832	-$10,835
Year 10	$36,845	$67,851	-$13,155

The nominal column is the amount you would need at that date to buy exactly what the original amount buys today.

Nominal vs real value

The nominal amount stays flat; its purchasing power does not.

Real value at different inflation rates

What $50,000 is worth after 10 years across a range of inflation outcomes.

Canonical equations

The exact relationships implemented by this engine.

V_real = V_nom / (1 + π)ⁿ · deflating by the price index

(1 + r) = (1 + r_real)(1 + π) · exact; r_real ≈ r − π only for small rates

r_real = (1 + r(1−t))/(1 + π) − 1 · tax is levied on the nominal return

r_nom = π/(1−t) · the nominal return that just preserves purchasing power after tax

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Inflation is a discount rate applied to money itself. This engine deflates a nominal amount into today’s purchasing power, then works out the nominal return you need just to stand still after tax — a number that is usually higher than people expect.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the amount you want to test.

Set the inflation assumption. Use a rate that matches your actual spending mix, not the headline index.

Choose the horizon in years.

Add the nominal return on your capital to see the real return.

Enter your tax rate on nominal gains — tax is charged on the inflation component too.

Read the break-even nominal return: anything below it loses purchasing power.

The formula

V_{\text{real}} = \frac{V_{\text{nom}}}{(1+\pi)^n}, \qquad (1+r_{\text{real}}) = \frac{1+r_{\text{nom}}}{1+\pi}, \qquad r_{\text{nom}}^{*} = \frac{\pi}{1-t}

Reference: Fisher (1930), "The Theory of Interest"; standard CPI deflation practice.

Worked example

$50,000 over 10 years at 3.1% inflation (default inputs)

Inputs

Amount $50,000.
Inflation 3.1% per year over 10 years.
Nominal return 5%; tax on gains 22%.

Calculation path

1
Price index: 1.031^10 = 1.3570.
2
Real value: 50,000 / 1.3570 = $36,845.
3
Purchasing power lost: $13,155, or 26.3% of the original amount.
4
Real return on capital: 1.05 / 1.031 − 1 = 1.84%.
5
Break-even nominal return after 22% tax: 0.031 / 0.78 = 3.97%.

Result

Real value $36,845 · 26.3% of purchasing power lost · real return 1.84% · break-even nominal return 3.97%.

Interpreting the result

The important number is the last one: 3.97%. Any nominal return below that, after tax, leaves you poorer in real terms even though the account balance grew. At a 5% nominal return and 22% tax, you are earning 1.84% real — barely ahead of inflation, and that assumes the inflation assumption is right.

Assumptions & limitations

A single constant inflation rate applies to everything. Real baskets inflate unevenly — housing, healthcare and education typically outrun the headline index.

Tax is charged on the whole nominal gain, including the part that merely keeps pace with inflation.

The amount is not spent during the period; spending changes the compounding base.

No investment fees are deducted. A 1% fee on a 1.84% real return removes more than half of it.

Inflation is measured by a price index, which is an average — your personal rate depends on what you buy.

Frequently asked questions

Why not just subtract inflation from the return?

Subtraction is an approximation that only works for small rates. The exact relation is multiplicative: (1+r_real) = (1+r_nom)/(1+π). At 10% nominal and 8% inflation, subtraction gives 2% but the true real return is 1.85%.

Which inflation measure should I use?

CPI-U is the common default, but your personal inflation depends on your basket. If you rent, travel and pay for childcare, your rate is probably higher than the headline. Use a rate that reflects your spending.

How does this apply to a pension or annuity?

A fixed nominal pension loses purchasing power every year. Deflate the payment by (1+π)^n to see what it is worth in today’s money at the point you receive it.

Why does tax make inflation worse?

Because tax is levied on nominal gains. If inflation is 3% and your return is 3%, you have zero real gain but still owe tax on the nominal 3% — a real loss. The break-even nominal return is therefore π/(1−t), not π.

Is deflation possible in this model?

Yes. Enter a negative inflation rate and the real value rises. Persistent deflation is rare and usually accompanies recession, so treat the output as arithmetic rather than forecast.

Does this account for wage growth?

No. It compares an amount against prices. Real wage growth is the gap between your nominal raise and inflation, which is the same Fisher calculation applied to income.