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Define what the price index measures
A nominal investment gain and a rise in a chosen price index need matching dates and currency context. The resulting real return refers to that index, which may not match an individual’s spending basket. No tax treatment is implied by inflation adjustment.
Divide the growth factors
If nominal wealth grows by 8% while the index grows by 5%, real growth is 1.08/1.05−1 = 2.857143%. Subtracting 5% from 8% gives an approximate 3% under a different calculation.
The price-index factor 1+π must be positive.
Reconstruct nominal growth
Multiplying (1+rreal) by (1+π) returns nominal growth. This includes an interaction term that the simple difference omits. The gap becomes easier to see when the input changes are large.
Match periods before comparing
An annual nominal rate and a six-month inflation change are not directly compatible in this equation. Establish the common period or convert on an explicitly stated basis. Historical inflation adjustment does not predict the next period’s purchasing-power return.