Answer:
The bond will sell at a discount of $18,539.16.
Explanation
First, get the present value of the principal.
PRESENT VALUE OF PRINCIPAL =
BOND FACE VALUE / ((
1 +
MARKET INTEREST RATE) ^
YEARS)
$53,556.48 = $86,000.00 / ((1 + 0.07) ^ 7)
Next, get the dollar value of an end-of-period payment.
PAYMENT =
BOND FACE VALUE * (
1 +
STATED INTEREST RATE)
$2,580 = $86,000.00 * (1 + 0.03)
Next, get the present value of the periodic payments.
PRESENT VALUE OF INTEREST PAYMENTS =
PAYMENT *
PRESENT VALUE FACTOR AT MARKET RATE$13,904.37 = $2,580 * 5.39
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$67,460.84 = $53,556.48 + 13,904.37
Finally, Find the difference between the present value of the bond, and its initial cost. If the present value is higher, then people will pay a
premium for it. Otherwise, people will demand a
discount.
DIFFERENCE =
PRESENT VALUE OF BOND -
BOND FACE$-18,539.16 = $67,460.84 - 86,000.00