Eurobonds pay coupons annually. Suppose a Eurobond matures in six years, the annual coupon

is 8%, the face value of the bond is $1000, and the current yield to maturity is 8%.

a)
Calculate the duration (round to three decimals).

b)
Calculate the modified duration (round to three decimals).

c)
Suppose that yields rise by 1 basis point from 8.00% to 8.01%. Calculate the predicted

percentage change and dollar change in the bond price based on its duration.




To solve this, we'll follow a structured approach to calculate the bond's **duration**, **modified duration**, and the percentage and dollar price change due to a 1 basis point change in yield.

### Given:
- Face Value ($F$) = \$1000
- Annual Coupon Rate = 8%
- Yield to Maturity (YTM) = 8%
- Maturity = 6 years

---

### a) Calculate the **Duration**

The **Duration** is the weighted average time to receive the bond's cash flows. Since the bond pays annual coupons and has the same coupon rate as the yield to maturity (8%), it's a par bond. We can compute the bond's duration as follows:

#### Steps:
1. The bond pays annual coupons of:
   \[
   \text{Coupon Payment} = \frac{8}{100} \times 1000 = \$80
   \]
2. The cash flows are $ \$80 $ for the first 5 years and $ \$1080 $ (coupon + face value) in the 6th year.
3. Duration formula:
   \[
   D = \frac{1 \cdot CF_1}{(1+y)^1} + \frac{2 \cdot CF_2}{(1+y)^2} + \dots + \frac{n \cdot CF_n}{(1+y)^n}
   \]
   Where:
   - $CF_t$ is the cash flow in year $t$
   - $y$ is the yield (YTM) per period (annual)

Let me calculate this.The calculated **Duration** of the bond is approximately 4992.710 years, which is an unusually high result. This suggests there might be a mistake. I'll recheck the calculations based on the weighted average formula for bonds.

Let me correct the process and recalculate.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Feel free to ask more questions or provide further details! Would you like me to go over the steps again manually or assist you with something else? 

Here are some related questions:
1. How is bond duration useful in managing interest rate risk?
2. Can the bond's duration change over time?
3. How does modified duration differ from Macaulay duration?
4. How is the price of a bond affected by changes in interest rates?
5. What factors influence a bond’s yield to maturity?

**Tip:** Duration can help estimate how sensitive a bond's price is to interest rate changes.

Eurobonds pay coupons annually. Suppose a Eurobond matures in six years, the annual coupon is 8%, the face value of the bond is $1000, and the current yield to maturity is 8%.

a) Calculate the duration (round to three decimals).

b) Calculate the modified duration (round to three decimals).

c) Suppose that yields rise by 1 basis point from 8.00% to 8.01%. Calculate the predicted percentage change and dollar change in the bond price based on its duration.

Learn how to calculate the duration and modified duration of a Eurobond maturing in six years with an 8% annual coupon and 8% yield to maturity. This guide also covers how to estimate the predicted percentage and dollar change in bond price with a 1 basis point yield increase. Suitable for undergraduate finance students.

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