Calculate the market value of a $10,000 bond that carries a coupon rate of 7% and has 11 years remaining to maturity. The current market rate on this bond is 9% compounded semiannually.

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The market value of a bond can be calculated using the present value of its future cash flows, which include the present value of its coupon payments and the present value of its face value at maturity. Given a $10,000 bond with a 7% annual coupon rate, 11 years to maturity, and a current market rate of 9% compounded semiannually, the coupon payment is $700 annually or $350 semiannually. The number of periods (n) is 11 years * 2 = 22, and the market rate per period (i) is 9% / 2 = 4.5% or 0.045 in decimal.The present value of the coupon payments (PVC) is calculated using the formula for an annuity: PVC = C * [(1 - (1 + i)^-n) / i], where C is the semiannual coupon payment. Substituting the values gives: PVC = $350 * [(1 - (1 + 0.045)^-22) / 0.045] ≈ $5,122.57.The present value of the face value (PVF) is calculated using the formula: PVF = F / (1 + i)^n, where F is the face value. Substituting the values gives: PVF = $10,000 / (1 + 0.045)^22 ≈ $3,499.43.Adding PVC and PVF gives the market value of the bond: ≈ $5,122.57 + $3,499.43 = $8,622.

Calculate the Market Value of a $10,000 Bond That Carries