Question

You paid $10,747 for a 15-year 5 percent coupon bond. If the yield to maturity of the bond is 4.9%, what is the face value (in $) of the bond?

Answer 1

Bond's Market Value = [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

$10,747 = [{5%*Face Value} * {(1 - (1 + 0.049)^-(15)) / (0.049)}] + [Face Value / {1 + 0.049}^15]

$10,747 = [(0.05 * Face Value) * {0.5121 / 0.049}] + [Face Value / 2.0494]

$10,747 = [0.5225 * Face Value] + [0.4879 * Face Value]

$10,747 = 1.0105 * Face Value

Face Value = $10,747 / 1.0105 = $10,635.85