Final answer:
To calculate the price of a bond, use the present value formula. In this case, the price of the bond with a $1,500 face value, 10% coupon rate, and five years to maturity is $1,156.31.
Step-by-step explanation:
To calculate the price of a bond, we use the present value formula. The present value of the face value of the bond is calculated by dividing the face value by (1 + (discount rate / 2))^2n, where n is the number of semiannual periods. The present value of the coupon payments is calculated by dividing the coupon payment by (discount rate / 2) and then multiplying it by (1 - 1 / (1 + (discount rate / 2))^2n). Adding the present values of the face value and coupon payments gives us the price of the bond.
In this case, the face value of the bond is $1,500, the coupon rate is 10%, the number of semiannual periods is 5*2=10, and the appropriate discount rate is 12%.
Using the present value formula, the present value of the face value is $1,500 / (1 + (0.12 / 2))^10 = $651.63. The present value of the coupon payments is ($1,500 * 0.10) / (0.12 / 2) * (1 - 1 / (1 + (0.12 / 2))^10) = $504.68. The price of the bond is the sum of the present value of the face value and the present value of the coupon payments, which is $651.63 + $504.68 = $1,156.31.