Colby & Company bonds pay semiannual interest of $50. They mature in 15 years and have a par value of $1,000. The market rate of interest is 8%. The market value of Colby bonds is (round to the nearest dollar)

Question

Quizplus · Accepted Answer

The correct answer is A because the market value of a bond is the present value of its future cash flows, which includes the semiannual interest payments and the par value at maturity. Using the formula for the present value of an annuity, we can calculate the market value of the Colby bonds as follows:PV = PMT * [1 - (1 + r/2)^(-n*2)] / (r/2) + FV / (1 + r/2)^n*2where:PV = present valuePMT = semiannual interest payment = $50r = annual market rate of interest = 8%n = number of years to maturity = 15FV = par value = $1,000Plugging in the values, we get:PV = $50 * [1 - (1 + 0.08/2)^(-15*2)] / (0.08/2) + $1,000 / (1 + 0.08/2)^15*2PV = $50 * [1 - (1.04)^(-30)] / 0.04 + $1,000 / (1.04)^30PV = $50 * 14.877 + $1,000 / 2.191PV = $743.85 + $456.15PV = $1,173 (rounded to the nearest dollar)

Colby & Company Bonds Pay Semiannual Interest of $50