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The problem asks for the 2-year rate based on expected one-year nominal interest rates for the next three years. Here’s how we can solve it:

Given one-year nominal interest rates:
- First year: 3.5% = 0.035
- Second year: 2.3% = 0.023
- Third year: 4.0% = 0.040 (though we do not need this directly for the 2-year rate calculation)

We are tasked with finding the 2-year interest rate, \( r_2 \).

To do this, we use the formula for the average interest rate over two years, considering the rates for each one-year period:

\[
(1 + r_2)^2 = (1 + r_1)(1 + r_2)
\]

Where:
- \( r_1 = 0.035 \) (first year rate)
- \( r_2 = 0.023 \) (second year rate)

Substitute the values:

\[
(1 + r_2)^2 = (1 + 0.035)(1 + 0.023)
\]

First, calculate the product on the right-hand side:

\[
(1 + 0.035)(1 + 0.023) = 1.035 \times 1.023 = 1.058805
\]

Now, solve for \( r_2 \):

\[
1 + r_2 = \sqrt{1.058805}
\]

Taking the square root:

\[
1 + r_2 = 1.0291
\]

Thus:

\[
r_2 = 1.0291 - 1 = 0.0291
\]

So the 2-year rate is **0.0291**, or 2.91%.

Would you like more details or have any other questions? Here are five related questions:

1. How would you compute a 3-year average rate using the given interest rates?
2. How does the expectation theory affect the yield curve in this scenario?
3. What would the 2-year forward rate starting in year 2 be?
4. How do different interest rate compounding frequencies affect the yield curve?
5. How can one interpret the yield curve's shape using these nominal rates?

**Tip:** When calculating average interest rates over multiple years, the geometric average (compounding) is key, not the arithmetic average.

You expect one-year nominal interest rates to be 3.5%, 2.3%, and 4.0% in each of the next three years, respectively. What rate do you expect to show up on the yield curve as the 2-year rate? Report your answer as an annual rate in decimal format and show four decimal places.

Learn how to calculate the 2-year rate based on one-year nominal interest rates of 3.5%, 2.3%, and 4.0% over the next three years. This step-by-step solution covers key finance concepts such as the geometric average and yield curve. Suitable for finance students.

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