Investments, tenth edition

   Real and Nominal Rates of Interest 

 An interest rate is a promised rate of return denominated in some unit of account (dollars, 

yen, euros, or even purchasing power units) over some time period (a month, a year, 

20 years, or longer). Thus, when we say the interest rate is 5%, we must specify both the 

unit of account and the time period. 

 Assuming there is no default risk, we can refer to the promised rate of interest as a 

risk-free rate for that particular unit of account and time period. But if an interest rate is 

risk-free for one unit of account and time period, it will not be risk-free for other units or 

periods. For example, interest rates that are absolutely safe in dollar terms will be risky 

when evaluated in terms of purchasing power because of inflation uncertainty. 

 

To illustrate, consider a 1-year dollar (nominal) risk-free interest rate. Suppose 

exactly 1 year ago you deposited $1,000 in a 1-year time deposit guaranteeing a rate 

of interest of 10%. You are about to collect $1,100 in cash. What is the real return on 

your investment? That depends on what money can buy these days, relative to what you 

 could  buy a year ago. The consumer price index (CPI) measures purchasing power by 

averaging the prices of goods and services in the consumption basket of an average 

urban family of four. 

 Suppose the rate of inflation (the percent change in the CPI, denoted by  i ) for the last year 

amounted to  i   5  6%. This tells you that the purchasing power of money is reduced by 6% 

a year. The value of each dollar depreciates by 6% a year in terms of the goods it can buy. 

Therefore, part of your interest earnings are offset by the reduction in the purchasing 

power of the dollars you will receive at the end of the year. With a 10% interest rate, after 

you net out the 6% reduction in the purchasing power of money, you are left with a net 

increase in purchasing power of about 4%. Thus we need to distinguish between a    nominal