Math Problem Statement

An investment had a nominal return of 10.2 percent last year. The inflation rate was 3.7 percent. What was the real return on the investment?

Multiple Choice

14.28%

5.90%

6.27%

6.96%

10.09%

Solution

To find the real return on an investment, we use the Fisher equation, which accounts for the impact of inflation. The formula is:

Real Return=1+Nominal Return1+Inflation Rate1\text{Real Return} = \frac{1 + \text{Nominal Return}}{1 + \text{Inflation Rate}} - 1

Given:

  • Nominal Return = 10.2% = 0.102
  • Inflation Rate = 3.7% = 0.037

Substitute the values into the equation:

Real Return=1+0.1021+0.0371\text{Real Return} = \frac{1 + 0.102}{1 + 0.037} - 1

Let's calculate it.

Real Return=1.1021.0371\text{Real Return} = \frac{1.102}{1.037} - 1 Real Return=1.06271=0.0627\text{Real Return} = 1.0627 - 1 = 0.0627

Converting to percentage:

Real Return=6.27%\text{Real Return} = 6.27\%

Therefore, the real return on the investment is 6.27%.

The correct answer is:

6.27%

Would you like more details or have any other questions?

Here are 5 related questions for deeper understanding:

  1. How does inflation impact the real return on investment?
  2. Can the real return ever be higher than the nominal return?
  3. How does compounding affect the real return over multiple years?
  4. What is the relationship between interest rates and inflation in real returns?
  5. How do you calculate nominal returns for multiple investment periods?

Tip: The real return reflects the true increase in purchasing power, while the nominal return doesn't account for inflation.

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Math Problem Analysis

Mathematical Concepts

Inflation
Nominal Return
Real Return
Percentage

Formulas

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

Theorems

Fisher Equation

Suitable Grade Level

Grades 10-12