The real interest rate is 3.0% and the inflation rate is 5.0%. What is the nominal interest rate?

3.00%

5.00%

8.15%

2.00%


To calculate the nominal interest rate, we can use the Fisher equation:

\[
(1 + r_{nominal}) = (1 + r_{real}) \times (1 + r_{inflation})
\]

Where:
- \( r_{nominal} \) is the nominal interest rate.
- \( r_{real} \) is the real interest rate.
- \( r_{inflation} \) is the inflation rate.

Given:
- Real interest rate (\( r_{real} \)) = 3.0% or 0.03
- Inflation rate (\( r_{inflation} \)) = 5.0% or 0.05

Step 1: Substitute the values into the Fisher equation:

\[
(1 + r_{nominal}) = (1 + 0.03) \times (1 + 0.05)
\]

Step 2: Calculate the right-hand side:

\[
(1 + r_{nominal}) = 1.03 \times 1.05 = 1.0815
\]

Step 3: Solve for the nominal interest rate:

\[
r_{nominal} = 1.0815 - 1 = 0.0815 \text{ or } 8.15\%
\]

The correct nominal interest rate is **8.15%**.

Would you like to explore this further or have any more questions?

---

1. What is the significance of the Fisher equation in finance?
2. How does the nominal interest rate affect loan repayments?
3. What are the practical applications of knowing the nominal interest rate?
4. How do central banks use nominal and real interest rates in policy-making?
5. What happens when the inflation rate is higher than the nominal interest rate?

**Tip:** Always ensure to convert percentages to their decimal form before performing calculations.

Learn how to calculate the nominal interest rate using the Fisher equation with a detailed step-by-step guide. Given a real interest rate of 3.0% and an inflation rate of 5.0%, find the nominal interest rate. This problem explores financial concepts and the application of mathematical formulas in economics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation