Real Interest Rate (Fisher Equation)

Earning 8% while prices rise 3% does not leave you 5% better off. The exact relationship, Irving Fisher's, is multiplicative: $1 + r_{\ ext{real}} = (1+i)/(1+f)$, which gives $1.08/1.03 - 1 = 4.854\%$. The rough subtraction overstates the gain by about fifteen basis points here, and the error grows quickly as either rate rises. At 15% nominal against 10% inflation the subtraction says 5% while the truth is 4.55%.

Turned around, it answers the contractor's question about escalation clauses. To clear a genuine 5% while inflation runs at 10%, the nominal rate has to be $1.05 \ imes 1.10 - 1 = 15.5\%$, not 15%. The same logic applies to multi-year service agreements, wage schedules and any long-dated quote: an escalator that merely matches inflation preserves your position and gains you nothing.