Question

A ​$24,000 bond with interest at ​7.1% payable​ semi-annually and redeemable at par is bought two years before maturity to yield 9.9% compounded​ semi-annually. Compute the premium or discount and the purchase​ price, and construct the appropriate bond schedule.

Answer 1

To calculate the premium or discount and purchase price, we need to determine the present value of the bond's future cash flows at the yield rate of 9.9% compounded semi-annually. The bond pays interest semi-annually, so there will be four cash flows.

Step-by-step explanation:

Premium or Discount and Purchase Price

To calculate the premium or discount, we need to determine the present value of the bond's future cash flows at the yield rate of 9.9% compounded semi-annually. The bond pays interest semi-annually, so there will be four cash flows.
At an interest rate of 9.9%, the present value factors for each cash flow are 0.9572, 0.9176, 0.8784, and 1.0. Multiply each cash flow by the corresponding present value factor and sum them to find the present value of the bond. The difference between the present value and the bond's face value of $24,000 will determine the premium or discount.
To calculate the purchase price, subtract the discount or add the premium from the bond's face value.

Constructing the bond schedule involves computing the interest payment for each period and accumulating the interest balances. In the first period, the interest payment is (0.071/2) * $24,000. For the subsequent periods, the interest payment is based on the remaining principal balance. The bond schedule shows the interest payments and the accumulated balances.