How it works
Inflation compounds like interest, in reverse. At a yearly rate i, prices after n years are (1 + i)^n times what they are today. So an amount of money buys less by the same factor:
worth in today's money = amount / (1 + i)^n
cost of the same things = amount × (1 + i)^nThe time it takes for prices to double at a steady rate is:
doubling time = ln(2) / ln(1 + i)A quick mental version is the rule of 72: divide 72 by the rate in percent. At 3%, 72 / 3 = 24 years, close to the exact 23.4.
A worked example
You keep 10,000 in cash for 20 years and prices rise 3% a year. 1.03^20 is about 1.806, so the same shopping costs about 18,061 by then. Your 10,000 buys what about 10,000 / 1.806 = 5,537 buys today: it has lost about 45% of its buying power, even though the number in the account never changed.
Choosing a rate
- Inflation differs by country and from year to year. Many central banks, including the European Central Bank, the Bank of England and the US Federal Reserve, aim for about 2% a year over time, but actual rates have been well above and below that.
- Your own inflation depends on what you buy. Rent, energy and food can rise faster or slower than the average.
- The calculator uses one steady rate. Try a few rates to see the range.
This is why long-term plans use real returns, after inflation. See how that works in the Coast FIRE calculator and the guide to compound interest.