Hypothetical worked example and primary educational references; not observed market data.
An index establishes a measuring scale
A price index expresses the price of a defined basket relative to a selected base. Its level is a measuring scale, not a currency amount and not automatically a percentage change. BLS provides ratio methods for using CPI values in purchasing-power calculations. If the base is one hundred and a later value is one hundred twenty, that particular ratio describes a twenty-percent increase from the base. But a move from one hundred twenty to one hundred thirty-five has a different percentage denominator. Always identify the beginning value. Reading the later index level alone cannot establish inflation over a chosen interval, because the comparison date supplies the scale for the change.
Supporting references: 1. BLS: Math calculations to better utilize CPI data
Deflate money by the price ratio
To express later nominal money in base-period purchasing-power units, multiply the nominal balance by the base index divided by the later index. The worked example uses a USD 15,000 balance and an invented base of one hundred. Its two rows use later indexes of one hundred twenty and one hundred thirty-five. The resulting values are not amounts that can be withdrawn from the bank; the nominal account still contains the same USD. They are translations into a common price basis. This distinction is useful when comparing a goal established years earlier with money accumulated today. It separates a change in the measuring unit from an actual transaction in the savings account.
Hypothetical worked example
Deflating the same balance with two invented indexes
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Base-period index is 100.
- Nominal balance at the comparison date is USD 15,000.
- Comparison indexes are hypothetical 120 and 135, not actual CPI observations.
Calculated result (base-period USD)
- 1. Index rises from 100 to 120
- 12,500.00
- 2. Index rises from 100 to 135
- 11,111.11
Expanded comparison scale, not zero-based. Range: 10,833.33 to 12,777.78, in the units above. Case numbers match the labels; no probability or time trend is implied.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Hypothetical scenario | Calculated result (base-period USD) |
|---|---|
| Index rises from 100 to 120 | 12500.00 |
| Index rises from 100 to 135 | 11111.11 |
Calculation details
- Index rises from 100 to 120
- 12,500.00 base-period USD
((15000 * 100) / 120) - Index rises from 100 to 135
- 11,111.11 base-period USD
((15000 * 100) / 135)
Inflating a target reverses the ratio
If a goal is specified in base-period money, multiply it by the later index divided by the base index to obtain the nominal amount needed for equal basket purchasing power. This is the reverse of deflating a balance. Using the wrong ratio shrinks a target when prices rise, producing a plan that moves in the opposite direction from its objective. A simple direction check prevents that mistake: rising prices should make a fixed real target require more nominal money. Conversely, they should make a fixed nominal balance represent less real money. These paired checks are often more revealing than a calculator's displayed decimals because they test whether the question itself was translated correctly.
The base year should not change the result
Rebasing an index rescales all its levels by the same constant. A purchasing-power ratio remains unchanged because that constant appears in both numerator and denominator and cancels. Therefore, changing the index's reference base should not change a properly calculated real value for the same dates and series. If it does, the worksheet may have mixed values from incompatible bases or used an index level as a direct percentage. This invariance is a valuable quality-control check. It does not allow mixing different baskets, geographic coverage, or index definitions. Those differences can alter economic meaning even when the arithmetic ratios look tidy and the reference-base labels happen to be identical.
Choose the index for the question
BLS's CPI questions and answers explain that an aggregate measure need not match every consumer's experience. A household with unusual spending weights may face a different price pattern. A goal involving tuition, travel, or one appliance may need a more specific price assumption than a broad basket. Use the ratio method as a framework while naming the measure's limits. The table's invented indexes make no statement about historical or expected US inflation. For an actual comparison, obtain consistent values for the same series and appropriate dates, explain the basket, and retain the nominal amount alongside the adjusted one. That gives the reader both the spendable balance and the context needed to interpret its purchasing power.
Supporting references: 2. BLS: Consumer Price Index questions and answers
Test another situationInflate the unpaid part of a price-based target
A separate hypothetical case. Its inputs differ from the main worked example above.
Inflate the unpaid part of a price-based target
Suppose a hypothetical purchase costs USD 2,400 when an invented matching price index equals 120. By the payment date, assume the same basket's index reaches 150. Maintaining the original purchasing objective requires USD 3,000, an increase of USD 600. If USD 1,800 is already available at payment time, the remaining nominal funding gap is USD 1,200. These values are not CPI observations. The trade-off is between retaining the original nominal budget and increasing contributions or reducing the quantity purchased. Deflating the saved balance answers how much it represents on the earlier basis; inflating the target answers how many current dollars the purchase requires.
Check the direction and the series together
BLS's index-ratio method supports moving monetary values between price bases. Before multiplying, label the amount's current price date and its intended comparison date. A rising index should enlarge an earlier real target when expressed in later nominal dollars. Rebasing both index levels by the same constant should leave that result unchanged. Neither check permits combining different baskets or using a broad index as evidence that a particular vendor will raise its price proportionally. Where a firm quotation is available, reconcile it with the index estimate and explain the difference instead of forcing the quoted amount to fit the aggregate adjustment.
Supporting references: 1. BLS: Math calculations to better utilize CPI data
Check this case’s calculations
- Updated nominal target
- 3,000.00 USD
((2400 * 150) / 120) - Price-basis increase
- 600.00 USD
(((2400 * 150) / 120) - 2400) - Endpoint funding gap
- 1,200.00 USD
(((2400 * 150) / 120) - 1800)
Limits of this additional case
- A matching index is assumed; actual purchase prices can depart materially from an aggregate basket.
Limits of this analysis
- Index coverage may not match personal purchases.
- Different series or index bases cannot be mixed without adjustment.
- The calculation does not identify prices of any specific future purchase.
Sources and scope
- BLS: Math calculations to better utilize CPI data
Index ratios support percentage-change and purchasing-power calculations.
Scope: US CPI educational mathematics; examples use invented index values.. Reference accessed 2026-10-06.
- BLS: Consumer Price Index questions and answers
CPI represents an aggregate consumer price measure rather than every household's experience.
Scope: US index methodology; no actual inflation observations used.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
