The real interest rate is the rate of return after adjusting for inflation. It’s the rate at which purchasing power grows rather than nominal dollars. The actual (or nominal) rate blends real growth with inflation.
The relationship is the Fisher equation:
where is the inflation rate over the same period. Solving for :
Expanded out: . For small rates, the cross-term is tiny and people often quote the approximation . (5% nominal minus 3% inflation gives about 2% real.) For larger rates the approximation breaks; use the exact form.
A worked example. Your bank pays 6% nominal interest. Inflation is running at 4%. Your real return is
So your purchasing power is actually growing at only 1.92%, not 6%. The other 4-ish percentage points just keep up with inflation. The approximation is close but slightly off.
The same Fisher relation holds for any rate of return:
- Real MARR: .
- Real IRR: .
When evaluating a project, work in either:
- Real dollars at the real MARR, or
- Actual dollars at the actual MARR.
Mixing them (real dollars at actual MARR, say) double-counts inflation and gives a misleading PW.
A common pitfall: projected cash flows in real estate, infrastructure, and long-life industrial projects are often stated in real (today’s-dollar) terms, while the firm’s published MARR is in actual (nominal) terms. Discount real cash flows at the nominal MARR and you penalise the project twice for inflation, underestimating its PW.
If you have a real MARR and a stream of actual-dollar cash flows (or vice versa), convert one before discounting. Mechanical check: are your numerator (cash flow) and denominator (discount factor) in the same units of purchasing power? If yes, you’re consistent.