What is the value of a $1,000 par value bond with 10 years left to maturity,a 9% coupon rate paid annually and 7.5% YTM?

Question

Quizplus · Accepted Answer

The value of a bond is calculated by discounting the future cash flows (coupon payments and the par value at maturity) back to the present using the yield to maturity (YTM) as the discount rate. In this case, the bond pays an annual coupon of 9% of the $1,000 par value, which is $90 per year, for 10 years, and then repays the $1,000 par value at the end. With a YTM of 7.5%, these cash flows discounted back to the present value at this rate will result in a bond price higher than its par value because the coupon rate is higher than the YTM. Calculating the exact value requires using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the par value at maturity). The correct calculation results in a value of approximately $1,102.96, indicating that the bond is priced at a premium to its par value.

What Is the Value of a $1,000 Par Value Bond