Assume that you can purchase a 15-year,$1,000 face value bond which pays interest on a semiannual basis,for $1,324.23.If the market's effective annual required rate of return is 8.16 percent (or 4 percent semi-annually),how much interest does this bond pay each year?
A) $64.81
B) $56.37
C) $117.50
D) $132.19
E) $126.48

Question

Quizplus · Accepted Answer

The bond's price is given as $1,324.23, and the effective annual required rate of return is 8.16%, which translates to a semi-annual rate of 4%. Since bond interest payments are typically fixed and the bond pays semiannually, we can use the present value of an annuity formula to find the annual interest payment. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value ($1,324.23), PMT is the payment per period (what we're solving for), r is the rate per period (4% or 0.04), and n is the total number of periods (15 years * 2 = 30 periods). Rearranging the formula to solve for PMT gives us PMT = PV / [(1 - (1 + r)^-n) / r]. Plugging in the numbers, we find that the semiannual payment is approximately $58.75. Since this is the semiannual payment, the annual interest payment is $58.75 * 2 = $117.50.

Assume That You Can Purchase a 15-Year,$1,000 Face Value Bond