Prices grow by the inflation rate every year, and each year's rise is applied to the already-higher price, so inflation compounds just like interest does.
Future cost = A × (1 + i)t · Purchasing power = A ÷ (1 + i)t
A — amount today
i — yearly inflation as a decimal
t — years
At 3% a year prices double in about 24 years; at 7% in about 10. That is why savings earning less than inflation lose value even though the balance keeps rising.
Common questions
What inflation rate should I use?
Use your central bank's target (often 2%) for long periods, or the latest yearly consumer price inflation for your country for short ones.
How do I know if my savings keep up with inflation?
Compare your interest rate with inflation. The real return is roughly the interest rate minus the inflation rate; if it is negative, your money is losing buying power.