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.