Answer:
The bond will sell at a premium of $7,940.08.
Explanation
First, get the present value of the principal.
PRESENT VALUE OF PRINCIPAL =
BOND FACE VALUE / ((
1 +
MARKET INTEREST RATE) ^
YEARS)
$35,179.77 = $59,000.00 / ((1 + 0.09) ^ 6)
Next, get the dollar value of an end-of-period payment.
PAYMENT =
BOND FACE VALUE * (
1 +
STATED INTEREST RATE)
$7,080 = $59,000.00 * (1 + 0.12)
Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS =
PAYMENT *
PRESENT VALUE FACTOR AT MARKET RATE$31,760.30 = $7,080 * 4.49
Next, add the present value of the principal to the present value of all of the interst payments.
PRESENT VALUE OF BOND =
PRESENT VALUE OF PRINCIPAL +
PRESENT VALUE OF INTEREST PAYMENTS$66,940.08 = $35,179.77 + 31,760.30
Finally, Find the difference between the present value of the bond, and its initial cost. If the present value is higher, then people will pay a
premium for it. Otherwise, people will demand a
discount.
DIFFERENCE =
PRESENT VALUE OF BOND -
BOND FACE$7,940.08 = $66,940.08 - 59,000.00