Final answer:
The book value of a bond at the end of a certain year is the present value of all future cash flows associated with the bond. In this case, the bond pays an annual coupon of 7% and has a face value of $1,000. To calculate the book value at the end of the 7th year, we need to discount the future cash flows to their present value using a discount rate of 7%.
Step-by-step explanation:
The book value of a bond at the end of a certain year is the present value of all future cash flows associated with the bond. In this case, the bond pays an annual coupon of 7% which is $70. The face value of the bond is $1,000 and it has a maturity of 15 years.
To calculate the book value at the end of the 7th year, we need to discount the future cash flows to their present value. Each future cash flow can be discounted using the formula:
Present Value = Cash Flow / (1 + r)^n
Where r is the discount rate and n is the number of years from the current year to the year of the cash flow. Assuming a discount rate of 7%, we can calculate the book value at the end of the 7th year as follows:
- Calculate the present value of the annual coupon payments for the remaining 8 years (15 - 7 = 8) using the discount rate of 7%.
- Calculate the present value of the final redemption value of $1,000 in 8 years using the discount rate of 7%.
- Add the present values of the coupon payments and the redemption value to get the book value at the end of the 7th year.
By applying the above calculations, the book value at the end of the 7th year would be the sum of the present values of the coupon payments and the redemption value.