se the data on Treasury securities in the following table to answer the​ question:
 Date
 1 year
 2 year
 3 year
​ 03/05/2010
 0.4​% 
 0.88​%
 1.47​%
 
             ​ Source: U.S. Department of the Treasury.
Assuming that the liquidity premium theory is​ correct, on March​ 5, 2010, what did investors expect the interest rate to be on  the​ one-year Treasury bill two years from that date if the term premium on a​ two-year Treasury note was 0.01​% and the term premium on a​ three-year Treasury note was 0.03​%?
The expected interest rate is 
  
enter your response here​%.  ​(Round your response to two decimal​ places.)

To determine the expected interest rate on the one-year Treasury bill two years from March 5, 2010, using the liquidity premium theory, we will need to apply the **expectations hypothesis formula** along with the provided liquidity premiums (term premiums).

### Step-by-step Process:

We are given the following information:
- **1-year Treasury rate (r₁)** = 0.40%
- **2-year Treasury rate (r₂)** = 0.88%
- **3-year Treasury rate (r₃)** = 1.47%
- **Liquidity premium for the 2-year Treasury (LP₂)** = 0.01%
- **Liquidity premium for the 3-year Treasury (LP₃)** = 0.03%

The liquidity premium theory suggests that the yield on a long-term bond includes both the expected short-term rates and a liquidity (or term) premium. We can use the following formula to determine the expected interest rate on a 1-year Treasury bill two years from now \((E(r₁^{2}))\):

\[
(1 + r₃)^3 = (1 + r₁) \times (1 + E(r₁^{1})) \times (1 + E(r₁^{2}))
\]
Where:
- \(r₁, r₂, r₃\) are the interest rates for the 1, 2, and 3-year bonds respectively (adjusted for their term premiums).
- \(E(r₁^{1})\) is the expected 1-year rate 1 year from today.
- \(E(r₁^{2})\) is the expected 1-year rate 2 years from today.

Let's calculate the expected rate!The expected interest rate on the one-year Treasury bill two years from March 5, 2010, is **2.18%**.

Would you like more details on the calculation or have any questions?

Here are 5 related questions to consider:
1. How does the liquidity premium theory differ from the expectations hypothesis?
2. Why do longer-term securities generally have higher interest rates?
3. How are term premiums determined in real-world markets?
4. What factors influence the changes in Treasury security yields?
5. How would the expected rate change if the liquidity premium was higher?

**Tip:** When working with interest rates, always ensure you're using the correct decimal form (e.g., 0.40% = 0.004) to avoid calculation errors.

Assuming that the liquidity premium theory is​ correct, on March​ 5, 2010, what did investors expect the interest rate to be on the​ one-year Treasury bill two years from that date if the term premium on a​ two-year Treasury note was 0.01​% and the term premium on a​ three-year Treasury note was 0.03​%? The expected interest rate is (enter your response here​%). ​(Round your response to two decimal​ places.)

Calculate the expected interest rate for a one-year Treasury bill two years from March 5, 2010, using the liquidity premium theory. This problem covers key financial concepts such as the expectations hypothesis and liquidity premiums, with a detailed step-by-step solution.

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