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Read two separate endpoint ratios
Nominal investment wealth grows from 100 to 108 over the supplied year. The fictional price index grows from 100 to 105 during that same year. The case uses that index as the purchasing-power reference, not an individual spending basket.
Express wealth in constant index units
The initial indexed wealth is 100/100 = 1. Ending indexed wealth is 108/105 ≈ 1.028571. Relative growth is 2.857143%. The different numeric levels of wealth and the price index cancel through their consistent ratios.
| Quantity | Factor |
|---|---|
| Nominal wealth | 1.08 |
| Price index | 1.05 |
| Real wealth | 1.08 / 1.05 = 1.028571 |
Inspect the subtraction approximation
8%−5% = 3% exceeds the exact result by about 0.142857 percentage points. The approximation omits the factor relationship. For small changes it can be close, but it remains a different numerical operation.
Name the index and period
Real return depends on the chosen price-index coverage and matched dates. This example does not establish any tax, currency-hedging or future-inflation result. Keep those questions separate when using the arithmetic in a broader report.