Assuming the Face Value of Bond = $1000
(a) Maturity = 4 years
Number of periods to maturity = n = 4 years |
Yield to Maturity = r = 7.1% = 0.071 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.071)-4]/0.071 + 1000/(1+0.071)4 = $966.2 |
Maturity = 8 years
Number of periods to maturity = n = 8 years |
Yield to Maturity = r = 7.1% = 0.071 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.071)-8]/0.071 + 1000/(1+0.071)8 = $940.52 |
Maturity = 30 years
Number of periods to maturity = n = 30 years |
Yield to Maturity = r = 7.1% = 0.071 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.071)-30]/0.071 + 1000/(1+0.071)30 = $877.15 |
(b) Maturity = 4 years
Number of periods to maturity = n = 4 years |
Yield to Maturity = r = 5.1% = 0.051 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.051)-4]/0.051 + 1000/(1+0.051)4 = $1035.38 |
Maturity = 8 years
Number of periods to maturity = n = 8 years |
Yield to Maturity = r = 5.1% = 0.051 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.051)-8]/0.051 + 1000/(1+0.051)8 = $1064.37 |
Maturity = 30 years
Number of periods to maturity = n = 30 years |
Yield to Maturity = r = 5.1% = 0.051 |
Face Value FV = $1000 |
Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61 |
Hence, Price of Bond = 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 = 61[1-(1+0.051)-30]/0.051 + 1000/(1+0.051)30 = $1151.99 |
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