Answer:
The bond will sell at a discount of $14,866.67.
Explanation
First, get the present value of the principal.
PRESENT VALUE OF PRINCIPAL =
BOND FACE VALUE / ((
1 +
MARKET INTEREST RATE) ^
YEARS)
$45,761.90 = $67,000.00 / ((1 + 0.1) ^ 4)
Next, get the dollar value of an end-of-period payment.
PAYMENT =
BOND FACE VALUE * (
1 +
STATED INTEREST RATE)
$2,010 = $67,000.00 * (1 + 0.03)
Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS =
PAYMENT *
PRESENT VALUE FACTOR AT MARKET RATE$6,371.43 = $2,010 * 3.17
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$52,133.33 = $45,761.90 + 6,371.43
Finally, Find the difference between the present value of the bond, and its initial cost. If the present value is higher, then people will pay a
premium for it. Otherwise, people will demand a
discount.
DIFFERENCE =
PRESENT VALUE OF BOND -
BOND FACE$-14,866.67 = $52,133.33 - 67,000.00