Nominal vs Real Interest Rates

A savings account paying 5 percent sounds like a clear win. But if prices are rising 6 percent a year, the goods that $100 could buy today will cost $106 next year, while your account only grew to $105. You earned interest and still lost purchasing power. The rate printed on the account is the nominal rate; the rate that actually matters for your buying power is the real rate, and the gap between them is inflation.

Think of running on a treadmill that's also moving backward under you. The number on the treadmill's speed display is your nominal effort — how fast your legs are turning over. But if the belt itself is sliding backward at nearly the same speed, your actual progress across the room (the real rate) is tiny or even negative, no matter how impressive the display looks.

The Fisher relationship

The exact link between the three rates, named after economist Irving Fisher, is:

$$(1 + r_{\text{nominal}}) = (1 + r_{\text{real}}) \times (1 + \pi)$$

In words: growing your money at the nominal rate for a year is the same as growing it at the real rate and having prices grow by the inflation rate $\pi$ — the nominal rate has to cover both the real gain and the erosion from inflation. For everyday rates, the commonly used shortcut drops the small cross-term:

$$r_{\text{real}} \approx r_{\text{nominal}} - \pi$$

Worked example

A bond pays a 5 percent nominal yield. Inflation over the same year runs at 6 percent. Using the exact Fisher equation: $1 + r_{\text{real}} = 1.05 / 1.06 = 0.9906$, so $r_{\text{real}} = -0.94\%$. The approximation gives $5\% - 6\% = -1\%$, close enough for most everyday use — the lender is losing purchasing power despite collecting a positive nominal coupon.

Now compare a period of low inflation: the same 5 percent nominal bond, but inflation runs at 2 percent. Exact Fisher: $1.05/1.02 = 1.0294$, so $r_{\text{real}} = 2.94\%$, versus the approximation's $5\% - 2\% = 3\%$. A materially positive real return, from an identical nominal rate — the entire difference in outcome came from inflation, not from anything the bond itself did differently.

high-inflation case 5% 6% -0.9%

low-inflation case 5% 2% +2.9%

nominal / real inflation

What this means in practice

Bond markets price this directly: Treasury Inflation-Protected Securities (TIPS) pay a real yield outright, while ordinary Treasuries pay a nominal yield, and the gap between the two on matching maturities — the breakeven inflation rate — is the market's implied forecast for future inflation. Central banks think in real terms too: the Fed doesn't set nominal rates in a vacuum, it aims for a real policy rate that is restrictive or accommodative relative to inflation, which is why a nominal rate that seems high can still be stimulative if inflation is running even higher (a negative real rate), and a nominal rate that seems low can be quite restrictive if inflation has fallen further (a positive real rate).

Savers and borrowers feel this asymmetrically. A borrower with a fixed-rate mortgage taken out before an inflation surge is quietly delighted: they keep paying the same nominal amount while inflation erodes the real value of what they owe, so the real interest rate on their debt can turn negative even though the nominal rate never changed. A saver holding cash in a low-yielding account during that same surge is the one absorbing the loss — the real value of their savings shrinks even as the account balance grows. This is also why unexpected inflation is often described as a transfer of wealth from lenders to borrowers: whoever locked in a fixed nominal rate before inflation rose gets the real rate they didn't plan for, at the other side's expense.

Key terms

• Nominal rate — the interest rate literally stated in a contract, unadjusted for inflation.
• Real rate — the nominal rate adjusted for inflation, reflecting actual change in purchasing power.
• Fisher equation — the exact relationship linking nominal rate, real rate, and inflation.
• Breakeven inflation rate — the gap between a nominal Treasury yield and a matching TIPS real yield, read as the market's inflation forecast.