Answer:
The bond will sell at a premium of $7,497.36.
Explanation
First, get the present value of the principal.
PRESENT VALUE OF PRINCIPAL =
BOND FACE VALUE / ((
1 +
MARKET INTEREST RATE) ^
YEARS)
$39,513.18 = $77,000.00 / ((1 + 0.1) ^ 7)
Next, get the dollar value of an end-of-period payment.
PAYMENT =
BOND FACE VALUE * (
1 +
STATED INTEREST RATE)
$9,240 = $77,000.00 * (1 + 0.12)
Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS =
PAYMENT *
PRESENT VALUE FACTOR AT MARKET RATE$44,984.19 = $9,240 * 4.87
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$84,497.36 = $39,513.18 + 44,984.19
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$7,497.36 = $84,497.36 - 77,000.00