Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:This image contains a mathematical problem related to interest rates. Here's the transcription and explanation:
**Question:**
If the effective annual interest rate is 9% per year and inflation is 3.8% per year, what is the true annual interest rate?
**Solution Steps:**
1. **Annual Interest Rate Formula:**
- The relationship is given by nominal interest and inflation.
2. **Monthly Effective Interest Rate (effm):**
- \( \text{effm} = (1 + 0.09)^{1/12} - 1 \)
- Calculated as \( \approx 0.007207 \) or 0.7207% monthly effective rate.
3. **Nominal Interest Calculation:**
- Nominal = \( 0.7207 \times 12 \approx 8.6484 \)
4. **True Annual Interest Rate:**
- True annual interest = \( 3.8 + 8.6484 = 12.448\% \)
This solution outlines the steps to calculate the true annual interest rate by considering both the given effective interest rate and the inflation rate.
Expert Solution
Step 1
Given
Effective annual interest rate =9% per year
Annual inflation rate =3.8% per year
True or real annual interest rate is the nominal interest rate minus the rate of inflation.
True annual interest rate = Nominal interest rate per year - inflation rate per year
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