At 5% inflation, when is your money worth half?

Question

Prices rise about 5\% a year, so each year your cash buys a little less. Solve in your head. Roughly how many years until a dollar's purchasing power falls to half? Aim: under 10 seconds.

Accepted Answer

Halving at 5\% decay is the mirror image of doubling at 5\% growth, so the same rule applies: \frac{72}{5} = 14.4 	ext{ years.} Check: purchasing power is (1/1.05)^{n}; setting it to 	frac12 gives n = \ln 2 / \ln 1.05 \approx 0.693 / 0.0488 \approx 14.2 years. Takeaway. The rule of 72 does not care whether something is compounding up or down, a 5\% gain doubles money and a 5\% loss halves it, both in about 14 years. It is a fast way to feel how quietly inflation eats savings.

At 5% inflation, when is your money worth half?

Your answer

More Mental Math questions