Answers
Question 1:
r = annual market rate = 8%
Face Value = $1,000
n = 21 years
Price of Zero Coupon Bond = Face Value / (1+r)^n
= $1,000 / (1+8%)^21
= $1,000 / 5.03383372
= $198.655747
Therefore, Price of Zero Coupon Bond is $198.66
Question 2:
Annual Coupon = 8.8%
Coupon Price = C = Face Value * annual Coupon = $1,000 * 8.8% = $88
n = 17 years
r = market rate = 6.8%
Price of Bond = [C * [1 - (1+r)^-n]/r] + [Face Value / (1+r)^n]
= [$88 * [1 - (1+6.8%)^-17]/6.8%] + [$1,000 / (1+6.8%)^17]
= [$88 * 0.673194991 / 0.068] + [$1,000 / 3.05992862
= $871.193518 + $326.805009
= $1,197.99853
Therefore, Price of bond is $1,198
Question 3:
Coupon rate = 9.4%
Coupon Price = C = Face Value * Coupon rate /2 = $1,000 * 9.4% = $57
n = 14*2 = 28 Semi annuals
r = semi annual market rate = 11.4% / 2 = 5.7%
Price of Bond = [C * [1 - (1+r)^-n]/r] + [Face Value / (1+r)^n]
= [$57 * [1 - (1+5.7%)^-28]/5.7%] + [$1,000 / (1+5.7%)^28]
= [$88 * 0.788212485 / 0.057] + [$1,000 / 4.72171364]
= $1,216.88945 + $211.787515
= $1,428.67696
Therefore, Price of bond is $1,428.68
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