Question

Calculating Real Rates of Return

If Treasury bills are currently paying 4.7 percent, and the inflation rate is 2.2 percent, what is the approximate real rate of interest? The exact real rate?

A) Approximate real rate: 2.5 percent, Exact real rate: 2.5 percent
B) Approximate real rate: 2.5 percent, Exact real rate: 2.7 percent
C) Approximate real rate: 2.7 percent, Exact real rate: 2.5 percent
D) Approximate real rate: 2.7 percent, Exact real rate: 2.7 percent

Answer 1

The approximate real rate of interest using the given nominal rate of 4.7% and inflation rate of 2.2% is 2.5%. The exact real rate calculated through the Fisher Equation is also approximately 2.5% after rounding.

Step-by-step explanation:

To calculate the approximate real rate of interest, you can use the formula:
Approximate Real Rate of Interest = Nominal Interest Rate - Inflation Rate. Given that the nominal rate, or Treasury bill rate, is 4.7% and the inflation rate is 2.2%, the approximate real rate would be 2.5% (4.7% - 2.2%).

Now, for the exact real rate, we use the Fisher Equation, which is defined as:
Exact Real Rate of Interest = (1 + Nominal Rate) / (1 + Inflation Rate) - 1. Inserting our numbers, we get (1 + 0.047) / (1 + 0.022) - 1, which results in an exact real rate of approximately 2.448%, or roughly 2.5% when rounded to the nearest tenth.

This means that the correct answer is A) approximating the real rate to 2.5% and the exact real rate to the same when rounded.