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?

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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!