A General Power bond with a face value of $1,000 carries a coupon rate of 9.0%, has 9 years until maturity, and sells at a yield to maturity of 8.0%. (Assume annual interest payments.)
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To find the price of the bond, you need to calculate the present value of its future cash flows. Here's how you can do it step by step:
1. Determine the annual interest payment: The bond has a face value of $1,000 and a coupon rate of 9.0%. The annual interest payment can be calculated as:
Annual interest payment = Face value * Coupon rate
= $1,000 * 9.0%
= $90
2. Calculate the present value of annual interest payments: Since the bond has 9 years until maturity, you need to calculate the present value of $90 paid annually for 9 years. To do this, you can use the formula for present value of an ordinary annuity:
Present value of annuity = Annual interest payment * (1 - (1 + Yield to maturity)^(-number of periods)) / Yield to maturity
Plugging in the values:
Present value of annuity = $90 * (1 - (1 + 0.08)^(-9)) / 0.08
= $90 * (1 - (1.08)^(-9)) / 0.08
= $90 * (1 - 0.51364) / 0.08
= $90 * 0.48636 / 0.08
= $546.81750
3. Calculate the present value of the bond's face value: The bond's face value is $1,000, which will be received at the end of the 9th year. To calculate the present value, you can use the formula for present value of a single amount:
Present value of single amount = Face value / (1 + Yield to maturity)^number of periods
Plugging in the values:
Present value of single amount = $1,000 / (1 + 0.08)^9
= $1,000 / (1.08)^9
= $1,000 / 1.999374
4. Add the present values of the annual interest payments and the face value to find the price of the bond:
Price of bond = Present value of annuity + Present value of single amount
= $546.81750 + $500.15666
= $1,046.97
Therefore, the price of the bond is approximately $1,046.97.