Final answer:
The book value of a bond is determined by the present value of future payments and the principal at the initial yield rate. For the bond in question, calculations would include coupon payments and the 5-year principal, considering the current market interest rates.
Step-by-step explanation:
The subject in question is related to the calculation of the book value of a bond after a certain number of interest payments. Specifically, we're interested in finding the book value of a $13,500 bond with a coupon rate of 6.50%, payable semi-annually, with a 5-year maturity, after 8 payments, where the yield at purchase was 5.80% compounded semi-annually.
To determine the book value after 8 payments, one must calculate the present value of the remaining payments and the principal amount at the yield rate when the bond was purchased. This involves discounting future cash flows back to their present values. Coupon payments would be calculated based on the coupon rate, and the present value of these payments along with the present value of the bond's face value must be taken into account.
In the example provided for clarity, the yield or total return includes both the interest payments and capital gains, and is affected by changes in the market interest rates. As explained, when interest rates increase, the selling price of the previously issued bonds at a lower interest rate will decrease, and vice versa.