Homework Answers
Number of years to maturity = n
Yield to Maturity = r = 7%
Annual Coupon Payment P = 5%*1000 = $50
Face Value FV = $1000
Value of Bond = PV = $843.20
Hence, PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n = P[1 - (1+r)-n]/r + FV/(1+r)n
=> 843.20 = 50[1 - (1+0.07)-n]/0.07 + 1000/(1+0.07)n
=> 843.20 = 714.29[1 - (1+0.07)-n] + 1000/(1+0.07)n
=> 843.20 = 714.29 - 714.29(1+0.07)-n + 1000(1+0.07)-n
=> (1+0.07)-n = (843.20 - 714.29)/(1000 - 714.29)
=> n = - ln((843.20 - 714.29)/(1000 - 714.29)) / ln (1+0.07) = 11.76 years
Number of years remaining to maturity when 3 coupons are paid = 11.76 - 3 = 8.76 years
Hence, Value of bond = P[1 - (1+r)-n]/r + FV/(1+r)n = 50[1 - (1+0.07)-8.76]/0.07 + 1000/(1+0.07)8.76 = 872.23 = $872
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