real interest rate

Also called: real rate, inflation-adjusted rate

The growth of purchasing power: (1 + n) ÷ (1 + i) − 1, where n is the nominal rate and i inflation. 10.78% with 8% inflation gives 2.57%. The shortcut n − i always overshoots, more so when inflation is high.

A nominal rate says how fast money grows; inflation says how fast prices grow. What you can buy grows by their ratio:

$r_{real} = \frac{1 + n}{1 + i} - 1$

A deposit at 10.78% after tax with 8% inflation gives 1.1078 ÷ 1.08 − 1 = 2.57% a year. The shortcut n − i = 2.78% is close here, but it always overshoots, and the error grows with inflation: at 40% nominal and 30% inflation the shortcut says 10%, the truth is 7.69%. A real rate can be negative: 6% with 8% inflation is −1.85%.

The same idea turns a future sum into today’s money: divide by (1 + i)ⁿ. That is deflating, the inflation twin of discounting. A future price grows the other way, p × (1 + i)ⁿ.

Example

150,000 UAH at 10.78% a year becomes 184,083 in two years. With 8% inflation:

In today’s money: 184,083 ÷ 1.08² = 157,821.
Real gain: 157,821 ÷ 150,000 = 1.052, which is 1.0257², so 2.57% a year.

Common mistakes

Subtracting at high inflation. n − i overstates the real rate.
Comparing before-tax rates. Take tax off first, then adjust for inflation.
Adding inflation over years. Three years of 8% is 1.08³ = 1.26, not 1.24.
Mixing periods. Monthly rates go with monthly inflation, yearly with yearly.

Learn it in the course

Real and nominal rates · Inflation and purchasing power, the real rate as a ratio of growth factors, why n − i is only a shortcut, deflating a future sum, and exchange spreads.
Loans and amortization · How a payment splits into interest and principal, months to repay, a flat fee against interest on the balance, and the real annual cost of a loan as its internal rate.
Discounting · Compounding in reverse: PV = FV ÷ (1 + r)ᵗ, NPV as a sum of discounted cash flows, IRR found by trial, the hurdle rate, and payback with linear interpolation.