Suppose 1-year, 2 year and 3 -year interest rates today are 3.6%, 4% and 4.4%, respectively. What's the expected 1-year interest rate two years from now according to the expectations theory?

The Expectations Theory states that long-term interest rates are an average of current and expected future short-term interest rates. Using this, we can determine the expected 1-year interest rate two years from now.

Given:
- 1-year rate today (\(r_1\)) = 3.6%
- 2-year rate today (\(r_2\)) = 4%
- 3-year rate today (\(r_3\)) = 4.4%

We want to find the expected 1-year interest rate two years from now, which we will denote as \(E(r_1^{(2)})\).

The relationship between rates according to the Expectations Theory is:

\[
(1 + r_3)^3 = (1 + r_2)^2 \times (1 + E(r_1^{(2)}))
\]

### Step-by-step:
1. Convert the interest rates into decimal form:
   \[
   r_1 = 0.036, \quad r_2 = 0.04, \quad r_3 = 0.044
   \]

2. Plug into the equation:
   \[
   (1 + 0.044)^3 = (1 + 0.04)^2 \times (1 + E(r_1^{(2)}))
   \]

3. Solve for \(E(r_1^{(2)})\).

Let's calculate this.The expected 1-year interest rate two years from now, according to the Expectations Theory, is approximately **5.20%**.

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How would the calculation change if interest rates followed different market expectations?
2. What is the difference between the Expectations Theory and the Liquidity Premium Theory?
3. How does the market react if future interest rates are expected to rise significantly?
4. What are the limitations of using the Expectations Theory in predicting interest rates?
5. Can the Expectations Theory explain the shape of the yield curve?

**Tip:** The yield curve provides a graphical representation of interest rates across different maturities and can signal expectations about future economic activity.

Suppose 1-year, 2-year, and 3-year interest rates today are 3.6%, 4%, and 4.4%, respectively. What's the expected 1-year interest rate two years from now according to the expectations theory?

Discover how to calculate the expected 1-year interest rate two years from now using the Expectations Theory. Learn step-by-step how today's 1-year, 2-year, and 3-year interest rates of 3.6%, 4%, and 4.4%, respectively, influence future interest rate predictions. Ideal for college students studying finance.

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