Find the price of a bond with a face value of $12,500 that pays an annual coupon of $750 for a period of 11 years. The discount rate is 8% pa. Give your answer in dollars and cents to the nearest cent.
To find the price of a bond, we need to calculate the present value of its future cash flows.
In this case, the bond has a face value of $12,500 and pays an annual coupon of $750 for a period of 11 years. The discount rate is 8% per year.
To calculate the present value of the coupon payments, we can use the formula for the present value of an ordinary annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value of the coupon payments
C = Coupon payment per period
r = Discount rate per period
n = Number of periods
In this case:
C = $750
r = 8% per year = 0.08
n = 11 years
Let's plug these values into the formula:
PV = $750 * [(1 - (1 + 0.08)^(-11)) / 0.08]
Now, let's calculate this value:
PV = $750 * [(1 - (1.08)^(-11)) / 0.08]
≈ $6,326.49
Next, we need to calculate the present value of the face value of the bond. Since it is paid at the end of the 11 years, we can simply discount it using the same discount rate:
PV_face_value = Face value / (1 + r)^n
Plugging in the values:
PV_face_value = $12,500 / (1 + 0.08)^11
≈ $5,343.57
Finally, to find the price of the bond, we sum up the present values of the coupon payments and the face value:
Price = PV + PV_face_value
≈ $6,326.49 + $5,343.57
≈ $11,670.06
Therefore, the price of the bond is approximately $11,670.06.