Nominal Interest Rate

A nominal rate measures growth in units of currency. Deposit 1,000 at a nominal 6% and you will have 1,060 in a year. Whether that leaves you better off depends on prices. If the goods you buy cost 4% more by then, your 1,060 buys only about 1.9% more than your 1,000 did: that is the real rate of return.

Lenders know this and price it in. The nominal rate on a loan includes compensation for the inflation expected over its life, on top of the real reward for lending and any premiums for risk. When inflation expectations rise, nominal rates tend to rise with them, even if nothing about the borrower has changed.

Nominal rate, real rate and expected inflation are linked multiplicatively: 1 + nominal rate = (1 + real rate) × (1 + inf), where inf is expected inflation. Rearranged, the real rate is (1 + nominal rate) / (1 + inf) − 1. The familiar shortcut, nominal rate minus inflation, ignores a small cross term and is accurate only when the numbers are small.

The gap grows with the level of rates. At 3% nominal and 1% inflation, the exact real rate is 1.98% against an approximation of 2%. At 40% nominal and 30% inflation, it is 7.7% against 10%. For continuously compounded rates the subtraction is exact, because logarithmic rates add.

Analysts often build an interest rate in layers: a real risk-free rate, plus compensation for expected inflation, which together give the nominal risk-free rate, plus premiums for default risk, liquidity and maturity. This additive framework is a standard approximation and is written with an approximately-equal sign. Yields on short-term government bills are the usual proxy for the nominal risk-free rate, because they carry minimal default and interest rate risk.

Consistency matters when discounting. Nominal cash flows, which include expected inflation, must be discounted at a nominal rate, and real cash flows at a real rate. Discounting forecasts stated in today's prices at a nominal rate systematically understates value.

Expect to convert between nominal and real rates exactly, to recognize when the subtraction shortcut is acceptable, and to compute a real return from a realized nominal return and realized inflation with the same formula. Expect also to explain what happens to nominal rates when inflation expectations change, and why an investor holding a fixed nominal bond loses when inflation turns out higher than expected.

A useful check: if inflation is higher than the nominal rate, the real rate is negative. Savers then lose purchasing power even while their account balances grow, a situation that persisted in many developed economies for long stretches after 2008 and again in 2022.