Question

Question 1

What is the price of a zero-coupon 21-year maturity bond per face (par) value of $1,000 if the annual market rates for these bonds are 8%?

Question 2

What is the price of a 17-year bond paying 8.8% annual coupons with a face (par) value of $1,000 if the market rates for these bonds are 6.8%?

Question 3

What is the price of a 14-year bond paying an annual coupon rate of 9.4%, but paying it semiannually, per face (par) value of $1,000 if the annual market rates for these bonds are 11.4%?

Answer 1

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