Math Problem Statement

What is the real interest rate given a nominal rate of 7.5​% and an inflation rate of 4.1​%?

Solution

To find the real interest rate, we can use the Fisher equation, which adjusts the nominal interest rate for inflation:

Real Interest Rate=(1+Nominal Rate)(1+Inflation Rate)1\text{Real Interest Rate} = \frac{(1 + \text{Nominal Rate})}{(1 + \text{Inflation Rate})} - 1

Given:

  • Nominal rate = 7.5% or 0.075
  • Inflation rate = 4.1% or 0.041

Substituting these values into the formula:

Real Interest Rate=(1+0.075)(1+0.041)1\text{Real Interest Rate} = \frac{(1 + 0.075)}{(1 + 0.041)} - 1

Calculating this:

Real Interest Rate=1.0751.04110.0326 or 3.26%\text{Real Interest Rate} = \frac{1.075}{1.041} - 1 \approx 0.0326 \text{ or } 3.26\%

Answer:

The real interest rate is approximately 3.26%.

Would you like further details or have any questions?


  1. How does the real interest rate impact savings and investments?
  2. How would a change in inflation affect the real interest rate?
  3. What is the Fisher equation and its applications in finance?
  4. How does a high nominal interest rate with low inflation compare in real returns?
  5. How does compounding affect the calculation of real interest?

Tip: Real interest rates provide a clearer picture of purchasing power changes over time, essential for long-term financial planning.

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Math Problem Analysis

Mathematical Concepts

Finance
Real Interest Rate Calculation

Formulas

Real Interest Rate = (1 + Nominal Rate) / (1 + Inflation Rate) - 1

Theorems

Fisher Equation

Suitable Grade Level

College Level