Math Problem Statement

Suppose an investment gave you a real rate of return of 10.50%. If the inflation rate was 13.00%, what was your nominal rate of return?

Solution

To calculate the nominal rate of return, we can use the following formula:

1+rn=(1+rr)×(1+i)1 + r_n = (1 + r_r) \times (1 + i)

Where:

  • rnr_n is the nominal rate of return
  • rrr_r is the real rate of return (10.50% or 0.105)
  • ii is the inflation rate (13.00% or 0.13)

Now, let's solve for rnr_n:

1+rn=(1+0.105)×(1+0.13)1 + r_n = (1 + 0.105) \times (1 + 0.13) 1+rn=1.105×1.13=1.248651 + r_n = 1.105 \times 1.13 = 1.24865 rn=1.248651=0.24865=24.865%r_n = 1.24865 - 1 = 0.24865 = 24.865\%

So, the nominal rate of return is approximately 24.87%.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the difference between nominal and real rates of return?
  2. How does inflation affect the nominal rate of return?
  3. If the inflation rate decreases, how would the nominal return be affected?
  4. How can the real rate of return remain positive even when inflation is high?
  5. What other factors besides inflation influence nominal returns?

Tip: The nominal rate of return is always higher than the real rate when inflation is positive.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inflation
Rates of Return

Formulas

1 + r_n = (1 + r_r) × (1 + i)
r_n = (1 + r_r) × (1 + i) - 1

Theorems

Fisher Equation (relation between nominal, real rates of return, and inflation)

Suitable Grade Level

Grades 11-12