guarantee- ing a rate of interest of 10%. You are about to collect $1,100 in cash. Is your $100 return for real? 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 aver- age urban family of four. Although this basket may not represent your particular consump- tion plan, suppose for now that it does. Suppose the rate of inflation (percent change in the CPI, denoted by i) for the last year amounted to i 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 interest rate-the growth rate of your money-and a real interest rate-the growth rate of your purchasing power. If we call R the nominal rate, r the real rate, and i the inflation rate, then we conclude   r R i   In words, the real rate of interest is the nominal rate reduced by the loss of purchasing power resulting from inflation. In fact, the exact relationship between the real and nominal interest rate is given by   1 R 1 r   1 i I. Introduction 5. History of Interest Rates and Risk Premiums The McGraw−Hill Companies, 2001           CHAPTER 5 History of Interest Rates and Risk Premiums 133     This is because the growth factor of your purchasing power, 1 r, equals the growth fac- tor of your money, 1 R, divided by the new price level, that is, 1 i times its value in the previous period. The exact relationship can be rearranged to   r R i 1 i