Short note: market vs inflation-free interest rate

Market interest rate (i)

The market (combined or nominal) interest rate is the rate actually quoted and earned or paid in the market, such as the bank loan rate or MARR. It contains compensation for inflation as well as the real return on capital, so it is used for actual-dollar cash flows.

Inflation-free interest rate (i')

The inflation-free (real) interest rate is the rate that would apply if there were no inflation, i.e. the true growth in purchasing power. It is used for constant-dollar cash flows.

Relationship

With general inflation rate f:

i = i' + f + i'f           (market rate)
i' = (i − f) / (1 + f)     (inflation-free rate)

Example: market rate 13%, inflation 5% → i' = (0.13 − 0.05)/1.05 = 7.62%. Conversely, if i' = 6% and f = 5%, then i = 0.06 + 0.05 + 0.003 = 11.3%.

Use

Both approaches give the same present worth if applied consistently. Mixing them (for example discounting constant-dollar cash flows at the market rate) is a common error that understates the value of a project.