How inflation erodes savings (and the rule of 72)

Inflation erodes savings by shrinking purchasing power even when the account balance stays the same. With a hypothetical 6% annual inflation rate, $10,000 of today’s goods-buying power becomes about $9,433.96 after one year and about $5,583.95 after ten years if that rate compounded every year and the cash balance never grew. Those rates are examples only, not a forecast. The percentage calculator helps with related percent steps; the exact purchasing-power formula is written below.

Exact erosion formula

purchasing_power = principal ÷ (1 + inflation_percent ÷ 100) ^ years

At sample 6%:

Loss of buying power after ten sample years ≈ $4,416.05 on that principal. The cash might still show 10,000 on a statement. The basket of goods it covers is smaller.

Worked example with the percentage tool

Percent of: 6% of 10,000 = 600. That is one year’s inflation slice if you think in “dollars of price rise on a 10,000 basket,” not the exact remaining power.

6% of 10,000 = (6 ÷ 100) × 10,000 = 600

Subtract percent (common shortcut): 10,000 − 6% = 9,400.

That shortcut is not the same as dividing by 1.06. Exact one-year power is 9,433.96. The gap is about $33.96. For one year the error is small. Over many years, chaining the wrong formula compounds the mistake. Prefer the division form for multi-year erosion.

Rule of 72: fast, then check the error

years_approx = 72 ÷ inflation_percent

years_exact_to_halve = ln(2) ÷ ln(1 + inflation_percent ÷ 100)

At 6%, the rule says 12 years to cut purchasing power in half. Exact math says about 11.90 years. The rule is slightly slow here. At 8%, rule and exact nearly match (9 vs ≈9.01). At 3%, the rule is about half a year long. Use the rule for a napkin estimate, then run the exact formula when the decision matters.

The same rule is often taught for doubling money at a growth rate. Under inflation it answers the mirror question: how long until cash buys about half as much, if the rate stays constant. Neither use turns a sample percent into a prediction.

Second case: same cash, different sample rates

Hold $10,000 for 10 years under three labeled examples:

Higher sample inflation leaves less power. None of these rows is “the” official rate. Change the percent and the table moves.

Common mistakes

• Treating a bank balance as unchanged lifestyle funding when prices rose.
• Using Subtract percent once for a ten-year story.
• Reading the rule of 72 as exact.
• Mixing a nominal interest rate with inflation without saying which question you asked.
• Quoting a sample classroom rate as if it were today’s CPI.

Inflation indexes themselves are published by statistical agencies and can use different baskets and methods. This article never substitutes for those publications. It only shows how a constant sample percent would shrink purchasing power if it applied every year without pause.

For growth that adds a percent each year on a balance, see simple vs compound interest explained. For plain “X% of Y,” see how to calculate percentages.

Halving power under the sample 6% path

Rule of 72 says about 12 years. Exact math says about 11.90 years. After 12 full years at constant sample 6%:

10000 ÷ (1.06)^12 ≈ 4,969.69

That is slightly under half (5,000), which matches a rule that was a little long: by year 12 you have already passed the exact halfway mark. After 11 years the power is about 5,267.88, still a bit above half. The exact crossing sits between year 11 and 12, near 11.90. Keep the rule for speed, keep the logarithm when you need the crossing.

Try the percent steps

Open the percentage calculator. Run Percent of with 6 and 10000. Run Subtract percent with the same inputs and compare 9,400 to the exact 9,433.96 one-year power above. Nothing is sent to a server.

If your cash earns interest, compare that growth rate to your inflation assumption in two separate columns before you celebrate. This page does not model after-tax returns or product fees.

A short habit that keeps napkin math honest: write the principal, the sample inflation percent, the years, and whether you used rule-of-72 or the exact power formula. Four labeled fields prevent a later reread from mixing 9,400 (subtract percent) with 9,433.96 (exact one-year power) as if they were the same checkpoint. When you share the ten-year $5,583.95 figure, attach “sample 6% compounded annually, cash balance unchanged” in the same sentence so the assumption travels with the number.