If Treasury bills are currently paying 5.75 percent and the inflation rate is 2.8 percent, what is the approximate and the exact real rate of interest?

Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.

To find the real rate of interest, we can use two methods:

1. **Approximate Real Rate of Interest:**
   The approximate real rate is calculated by subtracting the inflation rate from the nominal rate of interest.
   
   \[
   \text{Approximate Real Rate} = \text{Nominal Rate} - \text{Inflation Rate}
   \]

2. **Exact Real Rate of Interest:**
   The exact real rate takes into account compounding and is calculated using the following formula:
   
   \[
   \text{Exact Real Rate} = \frac{1 + \text{Nominal Rate}}{1 + \text{Inflation Rate}} - 1
   \]

Given:
- **Nominal rate** = 5.75% = 0.0575
- **Inflation rate** = 2.8% = 0.028

### Step 1: Approximate Real Rate
\[
\text{Approximate Real Rate} = 5.75\% - 2.8\% = 2.95\%
\]

### Step 2: Exact Real Rate
\[
\text{Exact Real Rate} = \left(\frac{1 + 0.0575}{1 + 0.028}\right) - 1
\]

Let's calculate the exact real rate of interest.The exact real rate of interest is approximately **2.87%**.

### Summary:
- **Approximate Real Rate** = 2.95%
- **Exact Real Rate** = 2.87%

Would you like more details on the calculations or have any questions?

Here are 5 related questions to expand your understanding:
1. How does inflation affect the real rate of interest?
2. What is the difference between nominal and real interest rates?
3. How would a higher inflation rate impact the exact real interest rate?
4. Can the real interest rate ever be negative, and if so, when?
5. What other factors besides inflation might influence interest rates?

**Tip:** Always differentiate between nominal and real interest rates when making long-term investment decisions, as inflation erodes purchasing power.

If Treasury bills are currently paying 5.75 percent and the inflation rate is 2.8 percent, what is the approximate and the exact real rate of interest? Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.

Learn how to calculate the approximate and exact real rate of interest when Treasury bills pay 5.75% and the inflation rate is 2.8%. This problem covers key concepts of real vs nominal interest rates and provides detailed calculations suitable for high school and college students.

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