Treasury bills are currently paying 8 percent and the inflation rate is 2.8 percent.

Problem 7-12 Calculating Real Rates of Return [LO4]

Treasury bills are currently paying 8 percent and the inflation rate is 2.8 percent.

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

Approximate real rate

%

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

Exact real rate

%

 

Explanation:

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

R ≈ r + h

Approximate r = .08 – .028

Approximate r = .052, or 5.20%

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 + .08) = (1 + r)(1 + .028)

r = [(1 + .08) / (1 + .028)] – 1

r = .0506, or 5.06%