An investment offers a total return of 13 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 8.5 percent. What does Janice believe the inflation rate will be over the next year?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

To find the inflation rate that Janice Yellen believes will occur over the next year, we can use the formula for the **real return** in relation to the **nominal return** and **inflation rate**:

\[
(1 + \text{Nominal Return}) = (1 + \text{Real Return}) \times (1 + \text{Inflation Rate})
\]

Where:
- Nominal return = 13% or 0.13
- Real return = 8.5% or 0.085
- Inflation rate = unknown

We solve for the inflation rate by rearranging the equation:

\[
1 + \text{Inflation Rate} = \frac{1 + \text{Nominal Return}}{1 + \text{Real Return}}
\]

\[
1 + \text{Inflation Rate} = \frac{1 + 0.13}{1 + 0.085}
\]

Now let's calculate the inflation rate.

\[
1 + \text{Inflation Rate} = \frac{1.13}{1.085} = 1.04138
\]

\[
\text{Inflation Rate} = 1.04138 - 1 = 0.04138
\]

Thus, the inflation rate is approximately:

\[
\text{Inflation Rate} = 4.14\%
\]

Janice believes the inflation rate over the next year will be **4.14%**.

Would you like any further clarification?

---

Here are 5 questions that expand on the concept:
1. What would the inflation rate be if the nominal return was 10% and the real return was 6%?
2. How is the real return affected if inflation increases by 1%?
3. Can real return ever exceed the nominal return? Under what circumstances?
4. How do different inflation rates impact investment strategies in real terms?
5. If inflation were 0%, how would the nominal and real returns compare?

**Tip:** Always distinguish between nominal and real returns—nominal includes inflation, while real adjusts for it!

An investment offers a total return of 13 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 8.5 percent. What does Janice believe the inflation rate will be over the next year?

Learn how to calculate the inflation rate when given a nominal return of 13% and a real return of 8.5%. This problem uses the relationship between real and nominal returns to estimate the inflation rate, applying important concepts in finance and algebra. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation