Valuing Bonds

Differences Between Real and Nominal Rates

Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation: $r = R - i$ or, $1+r = (1+r)(1+E(r))$ .

LEARNING OBJECTIVE

Differentiate between real and nominal interest rates

KEY POINTS

Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation.
Fisher equation states that the real interest rate is approximately the nominal interest rate minus the inflation rate: $1 + i = (1+r) (1+E(r))$ .
Simple equation between nominal rates and real rates: $i = R - r$ .

TERM

purchasing power
Purchasing power (sometimes retroactively called adjusted for inflation) is the amount of goods or services that can be purchased with a unit of currency.

In finance and economics, nominal rate refers to the rate before adjustment for inflation (in contrast with the real rate). The real rate is the nominal rate minus inflation. In the case of a loan, it is this real interest that the lender receives as income. If the lender is receiving 8% from a loan and inflation is 8%, then the real rate of interest is zero, because nominal interest and inflation are equal. A lender would have no net benefit from such a loan because inflation fully diminishes the value of the loan's profit.

The relationship between real and nominal rates can be described in the equation:

$(1+r)(1+i) = (1+R)$

Real and nominal: The relationship between real and nominal interest rates is captured by the formula. Where r is the real rate, i is the inflation rate, and R is the nominal rate.

The real rate can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate: $1 + i = (1+r) (1+E(r))$ , where $i$ = nominal interest rate; $r$ = real interest rate; $E(r)$ = expected inflation rate.

For example, if somebody lends $1,000 for a year at 10%, and receives $1,100 back at the end of the year, this represents a 10% increase in his purchasing power if prices for the average goods and services that he buys are unchanged from what they were at the beginning of the year. However, if the prices of the food, clothing, housing, and other things that he wishes to purchase have increased 20% over this period, he has in fact suffered a real loss of about 12% in his purchasing power.

In this analysis, the nominal rate is the stated rate, and the real rate is the rate after the expected losses due to inflation. Since the future inflation rate can only be estimated, the ex ante and ex post (before and after the fact) real rates may be different; the premium paid to actual inflation may be higher or lower.