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Easy Inflation & Purchasing Power

Are 100 euros today only worth half?

📖 The story

No currency change this time: many people feel that 100 euros today buy only what 50 euros bought 24 years ago. Which average annual inflation rate does that feeling imply? The same question works for dollars, francs or any other currency – the conversion rate is simply 1.

ℹ  Purchasing power estimated by feel; the official index rose less. Replace 50 with your own estimate – or with a real price then and now (a bread roll, a cinema ticket) to anchor the feeling.

Change any number and press "Calculate" – or use "Type in" on the right to watch it entered step by step.

What if …

Years in between × buys what once cost (old currency)
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What you learn

The inflation rate does not care about the currency: it is the n-th root of the price factor. Small annual rates halve purchasing power within a working life.

In short: A halving in 24 years needs only about 2.9 % a year – whatever the currency.
Formula
i = (amount · rate / then)^(1/n) − 1
With the example numbers
i = (100.00 · 1.00000 / 50.00)1/24 − 1 = (2.000)1/24 − 1 = 2.93 %
How to read the formula

The amount today is first converted into the old currency (amount × rate) and divided by what the same goods cost back then: that is the price factor. Its n-th root minus 1 is the average annual inflation rate – the same formula as for the return on a one-off investment, only with prices instead of capital. The odd rate of 1 € = 1.95583 DM was fixed irrevocably on 31 December 1998; it came from the value of the ECU, the basket of European currencies, on the last trading day. In everyday life it became "one euro is two marks". With the cash changeover in 2002 prices were converted in different ways: many were divided correctly by 1.95583 or rounded down in the customer's favour, but some everyday prices went straight from 1 DM to 1 € – hence the German nickname "Teuro" (from "teuer", expensive). This calculator checks whether the feeling holds: enter your own estimate under "buys what once cost"; for the same currency set the conversion rate to 1.

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