Final answer:
The purchase price of a $5,500 bond with a 3.00% coupon rate and a market yield of 4.50% is calculated by finding the present value of the semi-annual interest payments and the bond's face value at maturity. The total of these present values gives the purchase price. A purchase price below the face value indicates a discount, while a price above face value suggests a premium.
Step-by-step explanation:
To calculate the purchase price of the $5,500 bond with a 3.00% coupon rate payable semi-annually and a market yield rate of 4.50% compounded semi-annually, we will calculate the present value of future cash flows from the bond. The bond pays semi-annual interest payments, which are $5,500 x 3.00% / 2 = $82.50 every six months until maturity. As the bond will mature in 5 years, and there are 2 periods each year, there will be a total of 10 interest payments. In addition, the bondholder will receive the face value of the bond ($5,500) at the end of the 5 years.
To find the present value of the interest payments and the face value, we use the present value formula for each payment and sum them up:
- PV of Interest Payments = $82.50 x [(1 - (1 + 4.50% / 2) ^ -10) / (4.50% / 2)]
- PV of Face Value = $5,500 / (1 + 4.50% / 2) ^ 10
Once we have the present values, we add them together to find the total purchase price of the bond. This would give us the price that an investor would be willing to pay for the bond given the yield rate of 4.50% compounded semi-annually.
If the purchase price of the bond is less than the face value ($5,500), the difference is called a discount. If the purchase price is more than the face value, the difference is referred to as a premium.