Treasury bills are currently paying 7 percent and the inflation rate is 3.2 percent.

Problem 7-12 Calculating Real Rates of Return [LO4]
Treasury bills are currently paying 7 percent and the inflation rate is 3.2 percent.



a.
What is the approximate real rate of interest? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer
3.80%

b. What is the exact real rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answer
3.68%

Explanation
Explanation
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.



The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is:



R ≈ r + h



Approximate r = .07 – .032
Approximate r = .038, or 3.80%



The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:



(1 + R) = (1 + r)(1 + h)

(1 + .07) = (1 + r)(1 + .032)
r = (1 + .07)/(1 + .032) – 1
r = .0368, or 3.68%