Hypothetical worked example and primary educational references; not observed market data.
A balance and a basket measure different things
Nominal savings describes the number of USD held. Real savings describes what those units can purchase relative to a chosen price basis. BLS's CPI mathematics explains the use of index ratios for purchasing-power comparisons. This distinction means an account can pay interest and still lose buying capacity. It also means a flat balance can gain buying capacity if the relevant prices fall. The article uses invented price changes rather than reported inflation data. Choose the basket or index intentionally, because the phrase real return has no complete meaning without the price measure and comparison dates. A household saving for a particular purchase may care more about that item's price than a broad average.
Supporting references: 1. BLS: Math calculations to better utilize CPI data
Compare growth factors on the same horizon
The exact real growth factor is the nominal balance growth factor divided by the price growth factor. Subtract one and express the result as a percentage to obtain the real return. The numerator describes how much money grew; the denominator describes how much more expensive the purchasing unit became. In the example, the nominal balance grows five percent over one year. One row assumes a two-percent price rise, and the other assumes seven percent. All inputs share the same dates. Dividing a yearly balance factor by a monthly inflation factor would mix horizons and produce an uninterpretable result even if the calculator accepted every input without an error.
Hypothetical worked example
Nominal growth under two hypothetical price changes
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.
- Savings grows 5% over one year before fees or taxes.
- The relevant basket rises either 2% or 7%.
- Rates use the same one-year horizon and a fixed basket.
Calculated result (percent real return)
- 5% nominal growth, 2% price rise2.94
- 5% nominal growth, 7% price rise-1.87
Shared zero-based scale; negative values extend to the left.
- Lowest displayed value
- -1.87
- Highest displayed value
- 2.94
Hypothetical cases from the table below, in the stated units. Not market observations, a forecast or a recommended choice. Read the scenario assumptions before comparing.
| Hypothetical scenario | Calculated result (percent real return) |
|---|---|
| 5% nominal growth, 2% price rise | 2.94 |
| 5% nominal growth, 7% price rise | -1.87 |
Calculation details
- 5% nominal growth, 2% price rise
- 2.94 percent real return
(((1.05 / 1.02) - 1) * 100) - 5% nominal growth, 7% price rise
- -1.87 percent real return
(((1.05 / 1.0700000000000001) - 1) * 100)
Subtraction leaves out a denominator
Subtracting inflation from nominal growth is a convenient approximation when both rates are relatively small. The exact expression divides the nominal-minus-inflation difference by one plus inflation. The denominator matters because the gain or loss is being evaluated in the new price environment. With positive inflation, simple subtraction overstates the magnitude relative to the exact percentage when both use the same inputs. An approximation should be identified as such, especially when comparing closely spaced outcomes or larger price changes. The exact factor method also scales naturally to several years: accumulate nominal factors and price factors separately, then divide the cumulative totals. This avoids repeatedly treating the difference of rates as though it were itself exact.
The spending target can move independently
Suppose someone saves for equipment whose price changes differently from the broad consumer basket. A positive CPI-adjusted return does not guarantee progress toward that equipment purchase. Conversely, a negative broad real return might coexist with a falling equipment price. Use a general index for broad purchasing-power questions and a goal-specific price assumption for a defined purchase. The two should not be quietly substituted for each other. This is a planning boundary rather than a defect in inflation measurement. A transparent report can show both the account balance and the estimated number of units of the desired purchase it could buy. That presentation makes the economic objective clearer than an isolated nominal interest percentage.
Adjust the net amount that remains available
FINRA's return discussion recognizes that costs and inflation affect interpretation. For a spendable-savings calculation, start with the amount available after relevant charges and any applicable tax effects, then apply the price adjustment. This article excludes taxes and fees to isolate the nominal-versus-real relationship, so its figures are not an after-tax planning result. Do not assume a fixed tax treatment or a predictable future inflation rate from this example. Its value is the mechanism: growth in money and growth in prices must be compared as factors on matching horizons. Update both sides when the goal or date changes, and preserve the uncertainty around the chosen price basket rather than allowing a precise percentage to imply certainty.
Supporting references: 2. FINRA: Return and rate of return
Test another situationA charge can erase an apparent purchasing-power gain
A separate hypothetical case. Its inputs differ from the main worked example above.
A charge can erase an apparent purchasing-power gain
Assume hypothetical USD 2,000 grows by 5% over one year, with an external USD 60 charge deducted from the final resources. Spendable money becomes USD 2,040. If the relevant basket also becomes 2% more expensive over that same year, the final money represents exactly USD 2,000 in starting-date purchasing power. Gross nominal interest has not increased real resources after the charge. Keeping the fee outside the growth base until year-end makes the timing explicit. The trade-off is a positive displayed account gain against a cost that consumes the amount needed merely to keep pace with this particular price assumption.
Reconcile the real change with a transaction ledger
BLS's CPI mathematics uses index ratios for purchasing-power comparisons. Apply that ratio to net resources measured at the same endpoint, and keep external charges associated with the decision visible even if they appear on another statement. Adding a late contribution complicates the meaning of a real return: part of the increase is new saving whose exposure began later. Deflate each dated flow consistently when assessing household wealth changes. Also distinguish maintaining the basket's purchasing power from paying for one named item; a broad price measure can be appropriate for general consumption yet fail to track the specific purchase the saver intends.
Supporting references: 1. BLS: Math calculations to better utilize CPI data
Check this case’s calculations
- Net nominal resources
- 2,040.00 USD
((2000 * 1.05) - 60) - Net starting-date purchasing power
- 2,000.00 USD
(((2000 * 1.05) - 60) / 1.02)
Limits of this additional case
- The price basket and year-end external charge are hypothetical; actual tax effects and personal inflation differ.
Limits of this analysis
- A household's basket may differ from an aggregate inflation index.
- Taxes and charges can reduce nominal growth before adjustment.
- Future inflation and account yields are not known.
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.
- FINRA: Return and rate of return
Percentage return relates gain to the amount committed; inflation and costs affect interpretation.
Scope: US investor education; no portfolio or product recommendation.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
