Math Problem Statement

Question 12 You estimate that an investment of yours has generated a nominal rate of return of 14% p.a. Over that same period of time, inflation has increased at a rate of 4% p.a. Which of the following is closest to your real rate of return p.a.? (a) 8.65% (b) 9.62% (c) 11.76% (d) 17.52%

Solution

To calculate the real rate of return when given the nominal rate of return and the inflation rate, we use the Fisher equation, which adjusts for inflation as follows:

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

Where:

  • Nominal rate = 14% (0.14)
  • Inflation rate = 4% (0.04)

Now, plugging these into the formula:

Real Rate of Return=1+0.141+0.041\text{Real Rate of Return} = \frac{1 + 0.14}{1 + 0.04} - 1

Real Rate of Return=1.141.041\text{Real Rate of Return} = \frac{1.14}{1.04} - 1

Now let's compute this:

Real Rate of Return=1.096151=0.096159.62%\text{Real Rate of Return} = 1.09615 - 1 = 0.09615 \approx 9.62\%

So, the closest option to your real rate of return is (b) 9.62%.

Would you like more details or have any questions?

Related questions:

  1. How does the Fisher equation account for inflation?
  2. What would happen if inflation was higher than the nominal rate of return?
  3. How is the nominal rate of return typically calculated for investments?
  4. Can the real rate of return be negative? What does that mean for an investment?
  5. How does compound inflation impact long-term investments?

Tip:

Always use the real rate of return to assess your investment's true profitability, as it accounts for the eroding effect of inflation.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Inflation Adjustment
Real Rate of Return

Formulas

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

Theorems

Fisher Equation

Suitable Grade Level

Undergraduate level (Financial Mathematics, Economics)