Clarington issued 15 year bonds in the amount of $500 000. Interest on the bonds is 2.2% payable annually. What is the issue price of the bonds, if the bonds are sold to yield 2.8% compounded quarterly?

Question

Quizplus · Accepted Answer

The issue price of the bonds can be calculated using the present value formula for bonds, which takes into account the present value of the bond's interest payments and the present value of the bond's principal amount at maturity. Given that the bond's annual interest rate is 2.2%, the annual interest payment is $500,000 * 2.2% = $11,000. The yield to maturity (market interest rate) is 2.8% compounded quarterly, which translates to a quarterly rate of 2.8% / 4 = 0.7%. The bond has 15 years to maturity, which equals 60 quarters. The present value of the interest payments (an annuity) can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], and the present value of the principal amount is calculated using the formula PV = F / (1 + r)^n, where PMT is the annual interest payment, r is the quarterly market rate expressed as a decimal, n is the total number of periods, and F is the face value of the bond. After calculating both present values and adding them together, the closest value to the calculated total present value is $461,954, making option C the correct answer.

Clarington Issued 15 Year Bonds in the Amount of $500