Question

A $4000, 7.0% bond redeemable at par in seven years bears coupons payable annually. Compute the premium or discount and the purchase price if the yield, compounded annually, is 5.5%, 6.5%, and 7.5%. -The purchase price of the 5.5% yield bond is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) -The 5.5% yield bond is sold at a premium of $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) -The purchase price of the 6.5% yield bond is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) -The 6.5% yield bond is sold at a premium of $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) -The purchase price of the 7.5% yield bond is $ (Round the final answer to the nearest cent as needed, Round all intermediate values to six decimal places as needed.) -The 7.5% yleld bond is sold at a discount of $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

The price of a bond is determined by its face value, coupon rate, yield, and time to maturity. To calculate the price of a bond for different yields, you calculate the present value of its coupon payments and its face value, then sum those values. Whether the bond is sold at a premium or discount depends on whether the price is above or below its face value.

Step-by-step explanation:

When calculating the price of a bond, we must consider the face value, coupon rate, yield (discount rate), and the number of periods until maturity. The bond in question is a $4000 bond with a 7.0% coupon rate and a 7-year term. The annual coupon payment is calculated as 7% of $4000, which gives us $280 per year.

To find the purchase price for different yields, we use the present value formula for an annuity (coupon payments) plus the present value of the bond's face value (which will be paid at maturity). For the bond with a 5.5% yield, we compute:

• The present value of the annuity (coupon payments): $280 x [(1 - (1 + 0.055)^-7) / 0.055]
• The present value of the face value: $4000 x (1 + 0.055)^-7

The sum of these two amounts gives us the purchase price of the bond. If the purchase price is above $4000, the bond is sold at a premium; if it is below $4000, the bond is sold at a discount. We repeat this calculation for the 6.5% and 7.5% yield bonds.

To answer the student's question, you will finish these calculations using a financial calculator or spreadsheet software, providing the purchase prices and indicating whether each is at a premium or discount.