Answer:
The bond was sold at $1,136.78.
Explanation:
Annual coupon = Bond face value * Coupon rate = $1000 * 5% = $50
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = semi-annul interest rate = 4% / 2 = 2%, or 0.02
n = number of period = 20 years * Number of semiannuals in a year = 20 * 2 = 40 semi-annuals
Substituting the values into equation (1), we have:
Annual coupon discount factor = ((1-(1/(1 + 0.02))^40)/0.02) = 27.3554792407382
Present value of coupon = (Annual coupon * Annual coupon discount factor) / 2 = ($50 * 27.3554792407382) / 2 = $683.886981018455
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.02)^40 = $452.890415185236
Therefore, we have:
Price of bond = Present value of coupon + Present value of the face value of the bond = $683.886981018455 + $452.890415185236 = $1,136.77739620369
Approximating to 2 decimal places, we have:
Price of bond = $1,136.78
Therefore, the bond was sold at $1,136.78.
