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For instance, if a loan offers a 4% nominal interest rate and inflation is 2%, the real interest rate is approximately 2%. The world of finance has a somewhat different definition.
The real return on a bond is roughly equivalent to the nominal interest rate minus the expected inflation rate. But if actual inflation exceeds expected inflation during the life of the bond, the bondholder's real return will suffer. This risk is one of the reasons inflation-indexed bonds such as U.S. Treasury Inflation-Protected Securities ...
To approximate the real interest rate, subtract the inflation rate from the nominal interest rate. For example, if the inflation rate is 5%, on a one-year loan of $1,000 with an 8% nominal ...
The equation is an approximation; however, the difference with the correct value is small as long as the interest rate and the inflation rate is low. The discrepancy becomes large if either the nominal interest rate or the inflation rate is high. The accurate equation can be expressed using periodic compounding as:
In this analysis, the nominal rate is the stated rate, and the real interest rate is the interest 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 interest rates may be different; the premium paid to actual inflation (higher or lower).
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 ...
In this equation, is the target short-term nominal policy interest rate (e.g. the federal funds rate in the US, the Bank of England base rate in the UK), is the rate of inflation as measured by the GDP deflator, is the desired rate of inflation, is the assumed natural/equilibrium interest rate, [9] is the natural logarithm of actual GDP, and ...
That is to say that, if and were constant or growing at equal fixed rates, then the inflation rate would exactly equal the growth rate of the money supply. An opponent of the quantity theory would not be bound to reject the equation of exchange, but could instead postulate offsetting responses (direct or indirect) of Q {\displaystyle Q} or of V ...