Final answer:
The price of a 2-year bond with a $100 face value, 3% annual coupon rate, and a 4.0% discount rate is approximately $99.08.
Step-by-step explanation:
The price of a bond can be calculated using the present value formula. The present value of future cash flows is calculated by discounting them using an appropriate discount rate. In this case, the bond has a 2-year maturity, a $100 face value, and a 3% annual coupon rate. The annual volatility of interest rates is 10%.
To calculate the price of the bond, we need to calculate the present value of the future cash flows. First, let's calculate the present value of the annual coupon payments:
- Year 1 coupon payment = $3 (3% * $100)
- Year 2 coupon payment = $3
Next, we need to calculate the present value of the face value payment at the end of Year 2:
- Face value payment at the end of Year 2 = $100
Now, we can discount these cash flows to their present value using the appropriate discount rate:
- Discount rate = r₁ = 4.0%
- Present value of Year 1 coupon payment = $3 / (1 + r₁) = $2.8846
- Present value of Year 2 coupon payment = $3 / (1 + r₁)² = $2.7740
- Present value of face value payment at the end of Year 2 = $100 / (1 + r₁)² = $93.4211
Finally, we add up the present values of all the cash flows to get the bond price:
- Bond price = Present value of Year 1 coupon payment + Present value of Year 2 coupon payment + Present value of face value payment at the end of Year 2
- Bond price = $2.8846 + $2.7740 + $93.4211 = $99.0797
Therefore, the price of the 2-year bond with a $100 face value, 3% annual coupon, and a 4.0% discount rate is approximately $99.08.