What does inflation do to purchasing power?

People type this into search every day: inflation purchasing power calculator.

Purchasing power is what a pile of money can buy. After prices rise, the same pile buys less. The inflation purchasing power calculator applies one annual rate you type, for a number of years you type. It does not look up the Consumer Price Index.

This page is a labeled model. It is not a forecast of next year’s prices, and it is not personalized financial advice.

One rate, compounded once a year

The formula is:

money today ÷ (1 + annual rate) ^ years

The result is labeled in today’s money. It is the buying power left if prices rise at that constant rate. The amount you still hold in the account is unchanged. What moved is the basket that cash can purchase.

Two extra lines come off that result.

Purchasing power lost is amount − power left.

Cumulative price increase is (1 + rate) ^ years − 1, printed as a percent. That is how much prices would have risen in the model, which is why the same cash covers a smaller share of the basket.

The BLS CPI overview describes the Consumer Price Index as the average change over time in prices of goods and services purchased for consumption by urban households. CPI-U covers over 90 percent of the population. Income taxes and investment items such as stocks, bonds, and life insurance are outside the index. User fees and sales taxes paid by the consumer are inside it.

The BLS purchasing power fact sheet converts dollars with a ratio of published index values. Their CPI inflation calculator does the annual version of that lookup. This site’s tool is the constant-rate formula above. A 3% input is a rate you chose for a plan. It is not a BLS release.

What BLS published for 2021 and 2022

On that fact sheet, the CPI-U U.S. city average all-items annual average is 270.970 for 2021 and 292.655 for 2022. BLS divides 270.970 by 292.655 and gets 0.926. Times 100, that is 92.6 percent. Their sentence: the purchasing power of a dollar in 2022 was about 92.6 percent of its purchasing power in 2021, a decline of about 7.4 percent.

The same page prices a basket with monthly indexes. December 2021 is 278.802. December 2022 is 296.797. The ratio 296.797 ÷ 278.802 is shown as 1.065. Then 1.065 × $500 = $532.50. BLS reads that as a basket that cost $500 in December 2021 costing $532.50 in December 2022.

Those figures are index arithmetic on published CPI levels. The examples below are the constant-rate calculator, on rates I typed so the steps are visible.

Example 1: $10,000 at 3% for 10 years

Calculator defaults:

• money today: $10,000
• average annual inflation: 3%
• years: 10

Price growth: 1.03 ^ 10 = 1.343916.

Power left: 10,000 ÷ 1.343916 = $7,440.94.

Lost: 10,000 − 7,440.94 = $2,559.06.

Cumulative price increase: 34.3916%, which prints as 34.4%.

Year 1 alone is 10,000 ÷ 1.03 = $9,708.74, a loss of $291.26, and a cumulative increase of 3%.

Year 2 is 9,708.74 ÷ 1.03 = $9,425.96. The tool’s two-year result is a loss of $574.04 and a cumulative increase of 6.1%, because 1.03 ^ 2 − 1 = 6.09%, which rounds to 6.1%. The second year’s loss is 9,708.74 − 9,425.96 = $282.78, smaller than year 1, because the 3% lands on a smaller remaining value.

Example 2: the same $10,000, four different rates

Hold $10,000 and 10 years. Change only the rate.

• 2%: 1.02 ^ 10 = 1.218994. Power $8,203.48. Lost $1,796.52. Cumulative 21.9%.
• 3% (the default): $7,440.94. Lost $2,559.06. Cumulative 34.4%.
• 4%: 1.04 ^ 10 = 1.480244. Power $6,755.64. Lost $3,244.36. Cumulative 48%.
• 6%: 1.06 ^ 10 = 1.790848. Power $5,583.95. Lost $4,416.05. Cumulative 79.1%.

One extra percentage point, from 3% to 4%, removes another 7,440.94 − 6,755.64 = $685.30 of purchasing power over these 10 years. From 2% to 6% the gap is 8,203.48 − 5,583.95 = $2,619.53.

Example 3: the same 3%, stretched over time

Hold $10,000 and 3%.

• 0 years: $10,000.00 left. Lost $0.00. Cumulative 0%.
• 5 years: 1.03 ^ 5 = 1.159274. Power $8,626.09. Lost $1,373.91. Cumulative 15.9%.
• 10 years: $7,440.94. Lost $2,559.06. Cumulative 34.4%.
• 15 years: power $6,418.62. Lost $3,581.38. Cumulative 55.8%.
• 20 years: power $5,536.76. Lost $4,463.24. Cumulative 80.6%.
• 25 years: power $4,776.06. Lost $5,223.94. Cumulative 109.4%.
• 30 years: 1.03 ^ 30 = 2.427262. Power $4,119.87. Lost $5,880.13. Cumulative 142.7%.

The second decade removes less than the first in dollars, and more than the first in percentage of what is left. From year 0 to year 10 the loss is $2,559.06. From year 10 to year 20 it is 7,440.94 − 5,536.76 = $1,904.18. From year 20 to year 30 it is 5,536.76 − 4,119.87 = $1,416.89. Each slice is about 25.6% of the value at the start of that decade, because 1 − 1 / 1.03 ^ 10 = 0.2559.

Example 4: a one-year edge, and a zero-rate edge

$1,000 at 3% for 1 year:

1,000 ÷ 1.03 = $970.87. Lost $29.13. Cumulative 3%.

The one-year case is the only horizon where “subtract 3%” matches the formula. 1,000 × 0.03 = $30, and the formula’s loss is $29.13, because you divide by 1.03 rather than multiplying the loss by 0.03 and subtracting. The gap is 30 − 29.13 = $0.87 on $1,000. It gets wider as the years stack. Example 5 is that stack at 10 years.

At 0% for 10 years the divisor is 1 ^ 10 = 1. Power left is $10,000.00. Lost is $0.00. Cumulative is 0%. The tool will sit still if you tell it prices sit still.

Example 5: the linear mistake

A common shortcut multiplies the rate by the years and subtracts once.

3% × 10 = 30 percentage points.

10,000 × (1 − 0.30) = $7,000.

The compounded result in example 1 is $7,440.94.

The shortcut removes an extra 7,440.94 − 7,000 = $440.94.

It does that because every later year is charged 3% of the original $10,000. In the formula, year 2 is charged 3% of $9,708.74. By year 10 the rate is landing on $7,440.94 of remaining power, not on the original pile. The percentage increase post is the one-step version of a price change. Multi-year inflation repeats that step.

The cumulative line is the right place for “how much did prices rise in total.” At 3% for 10 years that line is 34.4%, not 30%. Prices in the model are 1.3439 times the start, so the cash covers 1 / 1.3439 = 74.4% of the original basket.

Example 6: $50,000 over 20 years, and $100 over 40

Scale does not change the percent. It scales the dollars.

$50,000 at 3% for 20 years:

The 20-year factor is the same one that turned $10,000 into $5,536.76. Times 5, that is $27,683.79 left. Lost $22,316.21. Cumulative 80.6%, the same percent as the $10,000 row in example 3.

$100 at 3% for 40 years:

1.03 ^ 40 = 3.262038. Power 100 ÷ 3.262038 = $30.66. Lost $69.34. Cumulative 226.2%.

A $100 bill still says 100. In this model it buys what $30.66 bought on day one. I am not saying prices will follow 3% for 40 years. I am showing what the formula does when you type that.

Example 7: a grocery basket is one year, measured, not assumed

The grocery price change calculator uses two receipts, not a future rate.

Defaults: a basket that was $145 is now $158, and you shop 4 times a month.

Change per trip: 158 − 145 = $13.00.

Percent: 13 ÷ 145 × 100 = 8.9655, which prints as 9%.

Annual spending change: 13 × 4 × 12 = $624.00.

A smaller basket, $86 then $91, still 4 trips a month:

5 ÷ 86 × 100 = 5.814, which prints as 5.8%.

Per trip $5.00. Per year 5 × 4 × 12 = $240.00.

That 5.8% is a measured change between two baskets you typed. It is not the 3% planning rate in example 1, and it covers a year of trips rather than a decade of compounding. The grocery increase post stays on that receipt math.

Example 8: a savings balance, then a separate inflation step

The compound savings calculator grows a balance. Its assumptions exclude inflation. The compound interest post walks that tool with monthly deposits.

Here the deposit is zero, so the path is only the starting pile:

• starting balance: $10,000
• monthly contribution: $0
• annual return: 3%
• years: 10

The savings tool compounds monthly. The monthly rate is 3% ÷ 12. After 120 months the balance prints as $13,493.54. Contributed: $10,000.00. Growth: $3,493.54. Growth share: 25.9%.

A once-a-year 3% on the same $10,000 would be 10,000 × 1.03 ^ 10 = $13,439.16. The extra $54.38 is the monthly compounding inside the savings tool. Same 3% label, different schedule.

Type the printed balance into the inflation tool at 3% for 10 years:

• money today: $13,493.54
• rate: 3%
• years: 10

Power left: $10,040.46. Lost: $3,453.08. Cumulative price increase: 34.4%, the same percent as example 1.

The purchasing power sits a little above the original $10,000 because the savings tool compounded monthly and the inflation tool compounded yearly. If both steps used one annual 3%, 10,000 × 1.03 ^ 10 ÷ 1.03 ^ 10 would land on $10,000 exactly. Matching the two rates is an input choice for this example. It is not a prediction that a savings account will track inflation.

The constant-rate runs

Row 5 is the shortcut, not the calculator. The calculator’s matching row is example 1.

Open the inflation purchasing power calculator and type the rate you want to test. For a past basket, use a published index, or the grocery tool on two receipts you actually paid.