Math Problem Statement

An investment had a nominal return of 11.4 percent last year. The inflation rate was 3.8 percent. What was the real return on the investment?

Multiple Choice

6.82%

7.32%

15.63%

8.14%

11.23%

Solution

To find the real return on the investment, we can use the formula for real return:

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

  1. Convert percentages to decimals:

    • Nominal Return: 11.4%=0.11411.4\% = 0.114
    • Inflation Rate: 3.8%=0.0383.8\% = 0.038
  2. Plug values into the formula: Real Return=1+0.1141+0.0381\text{Real Return} = \frac{1 + 0.114}{1 + 0.038} - 1

  3. Calculate: Real Return=1.1141.03810.0732 or 7.32%\text{Real Return} = \frac{1.114}{1.038} - 1 \approx 0.0732 \text{ or } 7.32\%

Answer:

The real return on the investment is 7.32%.

Would you like more details or have questions about this calculation?


  1. How is the real return affected by higher inflation rates?
  2. What would happen to the real return if the nominal return decreased?
  3. Why is it important to consider real return rather than just nominal return?
  4. How does compounding impact real returns over multiple years?
  5. Can real return ever be negative, and what would that mean for an investment?

Tip: Real return gives a more accurate sense of purchasing power gained from an investment after adjusting for inflation.

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Math Problem Analysis

Mathematical Concepts

Finance
Inflation Adjustment
Real Return Calculation

Formulas

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

Theorems

Real Return Calculation Formula

Suitable Grade Level

Grades 10-12