Final answer:
The book value at the end of the 7th year is approximately $964.62. The interest portion in the 11th year represents 100% of the coupon payment.
Step-by-step explanation:
To calculate the book value at the end of the 7th year, we need to determine the remaining life of the bond. Since the bond has a maturity of 15 years and we are at the end of the 7th year, the remaining life of the bond is 15 - 7 = 8 years. On the 8th year, the bond will pay its final interest payment and the redemption value.
To calculate the book value at the end of the 7th year, we need to calculate the present value of the future cash flows. The cash flow consists of the annual coupon payment of 7% of $1000, which is $70, and the redemption value of $1000 at the end of the bond's life. We need to discount these cash flows to present value using an appropriate discount rate. Let's assume the discount rate is 6%. Using the present value formula, we can calculate the present value of the coupon payments over the remaining 8 years, which is $70 * (1 - (1 + 6%)^(-8))/6% = $70 * (1 - (1.06)^(-8))/0.06 ≈ $406.99. The present value of the redemption value is simply $1000 / (1.06)^8 ≈ $557.63. Adding the present values of the coupon payments and the redemption value gives us the book value at the end of the 7th year, which is approximately $406.99 + $557.63 = $964.62. Therefore, the book value at the end of the 7th year is approximately $964.62.
To calculate the percentage of the coupon which is the interest portion in the 11th year, we need to find the annual coupon payment for the bond at that time. Since the bond has a maturity of 15 years and we are in the 11th year, there are still 15 - 11 = 4 years remaining. The annual coupon payment is always 7% of the bond's face value, which is $1000 * 7% = $70. Therefore, the interest portion of the coupon payment in the 11th year is $70.
Now, we can calculate the percentage of the coupon which is the interest portion. The interest portion is $70 and the total coupon payment is $70 as well. So, the percentage is ($70 / $70) * 100% = 100%. Therefore, the interest portion in the 11th year represents 100% of the coupon payment.