Real interest rate

The real interest rate $i^{\prime }$ is the rate of return after adjusting for inflation. It’s the rate at which purchasing power grows, not just nominal dollars. The actual (or nominal) rate $i$ blends real growth with inflation.

The relationship is the Fisher equation:

$1+i=(1+i^{\prime })(1+f),$

where $f$ is the inflation rate over the same period. Solving for $i^{\prime }$:

$i^{\prime }=\frac{1+i}{1+f}-1.$

Expanded out: $i=i^{\prime }+f+i^{\prime }f$. For small rates, the cross-term $i^{\prime }f$ is tiny and people often quote the approximation $i^{\prime }\approx i-f$. (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

$i^{\prime }=\frac{1.06}{1.04}-1=0.01923\approx 1.92\%.$

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 $6-4=2\%$ is close but slightly off.

The same Fisher relation holds for any rate of return:

• Real MARR: ${\text{MARR}}_{\text{real}}=\frac{1+{\text{MARR}}_{\text{actual}}}{1+f}-1$.
• Real IRR: ${\text{IRR}}_{\text{real}}=\frac{1+{\text{IRR}}_{\text{actual}}}{1+f}-1$.

When evaluating a project, work in either:

• Real dollars at the real MARR, or
• Actual dollars at the actual MARR.

Mixing them — say, real dollars at actual MARR — 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. If you discount real cash flows at the nominal MARR, you’re effectively penalising the project twice for inflation, and you’ll underestimate its PW.

If you have a real MARR and a stream of actual-dollar cash flows (or vice versa), convert one before discounting. The simplest mechanical check: are your numerator (cash flow) and denominator (discount factor) using the same units of purchasing power? If yes, you’re consistent.

For the broader inflation context, see Inflation. For the time-value framework, see Time value of money and Minimum acceptable rate of return.