Final answer:
The current price of the bond can be found by calculating the present value of the annual interest payments using the present value of an annuity formula and summing it with the present value of the principal, which is discounted at the yield to maturity.
Step-by-step explanation:
The current price of the $1,000 par value bond with a coupon rate of 9%, annual coupon payments, 15 years to maturity, and an 11% yield to maturity can be calculated by finding the present value of its future cash flows. Those cash flows consist of 15 annual interest payments of $90 (9% of $1,000) and the final principal repayment of $1,000 at the end of the 15th year.
To calculate the present value of the annual interest payments, we use the formula for the present value of an annuity:
PV(Ann) = Pmt * [1 - (1 + r)^-n] / r
Where Pmt is the annual payment ($90), r is the yield to maturity (0.11), and n is the number of years (15). Using this formula:
PV(Interest Payments) = $90 * [1 - (1 + 0.11)^-15] / 0.11
Next, we calculate the present value of the principal repayment using the present value formula:
PV(Principal) = FV / (1 + r)^n
Where FV is the future value of the principal ($1,000). Applying the formula:
PV(Principal) = $1,000 / (1 + 0.11)^15
Now, we sum the present value of the interest payments and the principal repayment to get the current price of the bond.