In this guide
- Money growth and purchasing power answer different questions
- Match the values, index and period
- Divide the growth factors before subtracting one
- A quoted interest rate needs an inflation horizon
- Keep index coverage and other adjustments explicit
- Common questions about nominal and real return
- Sources and scope
Nominal return describes growth without adjusting for inflation. An index-relative real return adjusts that growth for the change in a declared price index. Both are rates expressed as proportions or percentages; the distinction is what the growth is measured against.
Money growth and purchasing power answer different questions
If a fictional value rises from 100 to 110 currency units (CU), its nominal return is 10%. That tells you how its money value changed. To measure purchasing power relative to a basket of goods and services, you also need the change in that basket’s price index over the same period.
The word nominal does not automatically mean before tax or before every cost. It identifies the absence of an inflation adjustment. Likewise, real does not tell you which fees or taxes have already been included. State those choices separately.
Match the values, index and period
Take one fictional investment observed at T0 and T1, with no money entering or leaving between them. Exclude distributions, fees, taxes and currency conversion. Define a fictional “Basket A price index” covering the same declared basket at both endpoints, with T0 as its base of 100. These are invented inputs, not current inflation or an account offer.
| Quantity | At T0 | At T1 | Growth factor |
|---|---|---|---|
| Nominal value | 100 CU | 110 CU | 110 / 100 = 11/10 |
| Basket A price index | 100 index points | 105 index points | 105 / 100 = 21/20 |
The index rises 5%. Keep its name, coverage and dates attached to that figure. A different basket or period answers a different purchasing-power question. The CPI guide’s series-label discussion explains why an index needs that context; it does not supply a current CPI input for this example.
Divide the growth factors before subtracting one
First compare growth factors: (110 / 100) / (105 / 100) = (11/10) / (21/20) = 22/21. Subtract one to get the real proportional return: 22/21 − 1 = 1/21. As a percentage, that is 100/21% ≈ 4.761904761…%. The proportion 1/21 and the percentage 100/21% express the same rate.
| Quantity | Calculation | Result |
|---|---|---|
| Nominal return | 110 / 100 − 1 | 1/10 = 10% |
| Basket A index change | 105 / 100 − 1 | 1/20 = 5% |
| Real growth factor | (11/10) / (21/20) | 22/21 |
| Real return | 22/21 − 1 | Proportion 1/21; percent 100/21% ≈ 4.761904761…% |
| Arithmetic rate difference | 10% − 5% | 5 percentage points; not the exact real return |
You can also express the endpoint in T0 purchasing-power units: 110 / (105 / 100) = 2200/21 CU, about 104.761904761… CU. Relative to the initial 100 CU, the increase is again about 4.7619%. This is an index-relative conversion, not a cash receipt.
Subtracting 5% from 10% gives a difference of 5 percentage points. It does not give the exact real return here because the growth factors must be divided. The exact calculation is (1 + nominal return) / (1 + index change) − 1, using the matched positive inputs in this example.
A quoted interest rate needs an inflation horizon
A nominal interest rate describes the interest charged on borrowing or credited on savings, rather than an arbitrary asset’s price gain. The Bank of England’s introduction to interest rates also distinguishes its policy rate from the rates offered to customers. Identify the actual contract, period and rate convention before adjusting for inflation.
Looking ahead uses an inflation expectation or assumption; looking back uses the inflation that occurred over the same period. These are often called ex ante and ex post comparisons. The Bank’s historical discussion of the Fisher relationship concerns expected inflation and notes the need to allow for compounding.
Consider a separate fictional one-year deposit: 100 CU receives exactly 5% interest, becoming 105 CU. Assume no other payments, fees, tax, default or currency conversion. Treat 5% as an effective rate for that year, and use one declared basket for both inflation comparisons.
| Question | Fictional basket change | Purchasing-power calculation |
|---|---|---|
| Before the year: what if the assumption holds? | Assumed 2% | 1.05 ÷ 1.02 − 1 ≈ 2.9412% |
| After the year: what occurred? | Realized 4% | 1.05 ÷ 1.04 − 1 ≈ 0.9615% |
The factor ratio is exact for each fixed inflation input; the displayed percentages are rounded. Subtracting the rates gives 3 or 1 percentage points, respectively, and only approximates these inflation-adjusted rates. The before-year row is conditional on its assumption. With uncertain inflation, putting its average forecast into the ratio does not generally give the exact expected real return. Neither row forecasts inflation or changes the earlier investment example.
Keep index coverage and other adjustments explicit
Basket A is the reference for this result. An average price index need not match an individual household’s spending, so its real-return figure is not automatically that household’s personal purchasing-power result. Neither endpoint forecasts future inflation.
Cash flows, investment income, fees, taxes and foreign-exchange changes need an explicit treatment in a real record. Two endpoint values alone do not describe arbitrary payments made on different dates. The discussion of horizon and turnover helps frame the period, while the currency quote record addresses a separate currency-reference question.
Choose the measurement for the question being asked: money growth or growth relative to a specified price index. This comparison does not identify a best investment, predict personal inflation or verify a product’s inflation protection.
Common questions about nominal and real return
Can nominal growth be positive while purchasing power falls?
Yes, if the matched price-index growth factor exceeds the nominal growth factor. That conclusion is relative to the specified index, not automatically to every household’s costs.
Why is 10% minus 5% not the exact real return?
The subtraction gives 5 percentage points. For these fixed inputs, dividing 1.10 by 1.05 and subtracting one gives 1/21, or about 4.7619%.
Does real return mean after tax and fees?
No. It identifies an inflation adjustment, without specifying which tax or cost adjustments have been made. The fictional example excludes both.
Can I treat a published CPI rate as my personal inflation rate?
Not automatically. Check the named series, coverage and period, and distinguish its basket from your own spending. No current CPI rate is used here.
What if I add or withdraw money during the period?
The simple endpoint calculation here no longer describes all of the inputs. The amounts and dates of those flows need a separately chosen measurement method; this example does not calculate it.
Explore HypaForecast markets
Browse market questions or check the current 5-minute and 15-minute BTC round details. These navigation links are separate from the fictional measurements in this guide.
Sources and scope
Interest-rate comparison sources checked on 20 October 2026. The Bank of England’s 1995 discussion is historical method context. The one-year deposit and both inflation inputs are fictional; the earlier investment example and its source scope remain unchanged.
- FINRA, Evaluating Performance (undated). Investor-education context for identifying investment return, income and costs.
- A. D. Wilkie, On the Calculation of Real Investment Returns, an archival author note hosted by the UK DMO. Relevant sections discuss observed purchasing-power calculations and separately consider multiple payments. The note’s publication date is unverified; its historical index and bond examples are not current product terms.
- Bank of England: What are interest rates?
- BoE Quarterly Bulletin May1995: Bond prices and market expectations of inflation
The Basket A inputs and worked calculations are original fictional examples. Their result depends on the stated matching and exclusions.
HypaForecast publishes educational guides and operates a prediction market. This purchasing-power example does not establish an inflation-linked HypaForecast feature, an offered return or your eligibility to trade.
Share this guide