rate" in an economy is often considered to be the rate of return on a risk-free investment, such as US Treasury notes, minus an index of inflation, such as the rate of change of the CPI or GDP deflator. Fisher equation The relation between real and nominal interest rates and the expected inflation rate is given by the Fisher equation where = nominal interest rate; = real interest rate; = expected inflation rate. For example, if somebody lends for a year at , and receives back at the end of the year, this represents a increase in her purchasing power if prices for the average goods and services that she 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 she wishes to purchase have increased over this period, she has, in fact, suffered a real loss of about in her purchasing power. (Notice that the approximation here is a bit rough; since 1.1/1.25 - 1 = 0.88 - 1 = -.12, the actual loss of purchasing power is exactly .) If the inflation rate and the nominal interest are relatively low, the Fisher equation can be approximated by After-tax real interest rate The real return actually gained by a lender is lower if there is a non-zero tax rate imposed on interest earnings. Generally taxes are imposed on nominal interest earnings, not adjusted for inflation. If the tax rate is denoted as t, the before-tax nominal earning rate is i, the amount of taxes paid (per dollar or other unit invested) is i × t, and so the after-tax nominal earning is i × (1–t ). Hence the expected after-tax real return to the investor, using the simplified approximate Fisher equation above, is given by Expected real after-tax return = Variations in inflation The inflation rate will not be known in advance. People often base their expectation of future inflation on an average of inflation rates in the past, but this gives rise to errors. The real interest rate ex-post may turn out to be quite different from the real interest rate (ex-ante real interest rate) that was expected in advance. Borrowers hope to repay in cheaper money in the future, while lenders hope to collect on more expensive money. When inflation and currency risks are underestimated by lenders, then they will suffer