What is the value of a 3-year (semiannual) Treasury note with an 8 % coupon rate and a face value of
$100? The spot rates are as follows. (Note: Spot rates are expressed as annualized rates on a bond-
equivalent yield basis.)
0.5 year: 2.4% 2 year: 5.4%
1 year: 4.2% 2.5 year: 5.6%
1.5 year: 4.8% 3 year: 6.2%

To find the value of a 3-year Treasury note with semiannual coupon payments, we need to calculate the present value of the coupon payments and the face value using the given spot rates.

### Given:
- **Coupon rate**: 8% annually (semiannual, so 4% per period)
- **Face value**: $100
- **Spot rates** (annualized bond-equivalent yields):
  - 0.5 year: 2.4%
  - 1 year: 4.2%
  - 1.5 year: 4.8%
  - 2 year: 5.4%
  - 2.5 year: 5.6%
  - 3 year: 6.2%

Since the bond pays semiannual coupon payments, we need to compute the present value for each of these cash flows. The bond pays $4 every 6 months (4% of $100 face value) and returns $100 at the end of 3 years along with the final coupon.

The formula for the present value (PV) of each cash flow is:

\[
PV = \frac{C}{(1 + r/2)^{2t}}
\]

Where:
- $C$ is the cash flow (coupon payment or face value),
- $r$ is the spot rate for the specific time,
- $t$ is the time in years.

Let’s now calculate the value of the bond.

### Cash Flows and Spot Rates:
1. **At 0.5 years**: $4 coupon, discount using 2.4% spot rate
2. **At 1 year**: $4 coupon, discount using 4.2% spot rate
3. **At 1.5 years**: $4 coupon, discount using 4.8% spot rate
4. **At 2 years**: $4 coupon, discount using 5.4% spot rate
5. **At 2.5 years**: $4 coupon, discount using 5.6% spot rate
6. **At 3 years**: $104 (coupon + face value), discount using 6.2% spot rate

Let's compute the present value of each of these payments.The value of the 3-year Treasury note, given the spot rates and an 8% coupon rate, is approximately **$105.19**.

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

Here are five related questions to consider:
1. How does the bond's price change if the spot rates increase?
2. What would the bond's price be if it had a different coupon rate?
3. How do semiannual payments affect the present value calculation compared to annual payments?
4. How is the bond's yield-to-maturity different from spot rates?
5. What is the significance of spot rates in bond pricing?

**Tip**: Spot rates are used to discount each cash flow from a bond individually, ensuring accurate bond pricing based on market rates for different maturities.

What is the value of a 3-year (semiannual) Treasury note with an 8% coupon rate and a face value of $100? The spot rates are as follows. (Note: Spot rates are expressed as annualized rates on a bond-equivalent yield basis.) 0.5 year: 2.4%, 1 year: 4.2%, 1.5 year: 4.8%, 2 year: 5.4%, 2.5 year: 5.6%, 3 year: 6.2%.

Discover how to determine the value of a 3-year Treasury note with an 8% coupon rate and $100 face value, using given spot rates. Learn step-by-step how to discount semiannual coupon payments and apply the present value formula. Spot rates include 0.5-year at 2.4%, 1-year at 4.2%, and more, leading to a bond valuation of approximately $105.19.

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