Math Problem Statement
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.
Solution
To find the real rate of interest, we can use two methods:
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Approximate Real Rate of Interest: The approximate real rate is calculated by subtracting the inflation rate from the nominal rate of interest.
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Exact Real Rate of Interest: The exact real rate takes into account compounding and is calculated using the following formula:
Given:
- Nominal rate = 5.75% = 0.0575
- Inflation rate = 2.8% = 0.028
Step 1: Approximate Real Rate
Step 2: Exact Real Rate
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:
- How does inflation affect the real rate of interest?
- What is the difference between nominal and real interest rates?
- How would a higher inflation rate impact the exact real interest rate?
- Can the real interest rate ever be negative, and if so, when?
- 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.
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Math Problem Analysis
Mathematical Concepts
Interest Rates
Inflation
Real vs Nominal Interest
Formulas
Approximate Real Rate = Nominal Rate - Inflation Rate
Exact Real Rate = (1 + Nominal Rate) / (1 + Inflation Rate) - 1
Theorems
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Suitable Grade Level
Grades 11-12 or College Level
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