Final answer:
The purchase price of the $19,000 bond is calculated by discounting its annual interest payments and par value at maturity at the desired yield rates. The bond's price will be at a premium if the yield rate is below the coupon rate, and at a discount if the yield rate is above it. The final purchase price is the aggregate present value of all cash flows.
Step-by-step explanation:
The question involves determining the purchase price of a bond with differing yield rates. To calculate the purchase price and whether the bond is bought at a premium or discount, we must discount the future interest payments and the principal repayment at the bond's maturity according to the desired yield rates. The present value (PV) of each cash flow must be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value of the cash flow, r is the yield rate, and n is the number of years until the cash flow occurs. Since the bond has a 5% coupon rate, it will pay an annual interest of $950 (5% of $19,000). For yield rates other than the coupon rate, the bond's price will differ from its face value, resulting in a premium or discount.
Part (a): When calculating the purchase price of a bond to yield 6% compounded annually, cash flows over the next 5 years are discounted at the 6% rate. For part (b), with a 4% yield, the same cash flows are discounted at the 4% rate, thus affecting the purchase price differently. To find the aggregate present value of all cash flows (interest payments and the par value at maturity), we add the present values of each individual cash flow.
The final answer will be the sum of the present values of the cash flows, which will provide the purchase prices at the different yield rates, indicating at what premium or discount the bond is purchased.