Question

Coupon rates. What are the coupon rates for the following bonds? Yield to Coupon Years to Coupon Frequency Par Value Maturity Maturity Price Rate $5,000.00 20 $3,925.15 monthly 1,000.00 5% $1,000.00 semiannual $1,000.00 9% $1,038.90 annual $1,000.00 11% $677.87 20 quarterly Hint: Make sure to round all intermediate calculations to at least six decimal places a. What is the coupon rate for the following bond? (Round to two decimal places.) Yield to Maturity Coupon Years to Coupon Frequency Par Value Maturitv ri $5,000.00 20 $3,925.15 monthly b. What is the coupon rate for the following bond? (Round to two decimal places.) Yield to Coupon Years to Coupon Maturity Par Value Maturit requency $1,000.00 8% $1,000.00 semiannual c. What is the coupon rate for the following bond? (Round to two decimal places.) Coupon Years to Yield to Coupon Maturity Par Value Maturit ice requency $1,000.00 $1,038.90 9% annual d. What is the coupon rate for the following bond? (Round to two decimal places.) Yield to Maturity Coupon Rate Years to Coupon Frequency Par Value Maturity Price 11% $677.87 $1,000.00 20 quarterly

Answer 1

a

K = Nx12

Bond Price =∑ [(Monthly Coupon)/(1 + YTM/12)^k]     +   Par value/(1 + YTM/12)^Nx12

k=1

K =20x12

3925.15 =∑ [(Coupon rate*5000/1200)/(1 + 7/1200)^k]     +   5000/(1 + 7/1200)^20x12

k=1

Coupon rate% = 25

b

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =15x2

1000 =∑ [(Coupon rate*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^15x2

k=1

Coupon rate% = 8

c

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

1038.9 =∑ [(Coupon rate*1000/100)/(1 + 9/100)^k]     +   1000/(1 + 9/100)^5

k=1

Coupon rate% = 10

d

K = Nx4

Bond Price =∑ [(Quarterly Coupon)/(1 + YTM/4)^k]     +   Par value/(1 + YTM/4)^Nx4

k=1

K =20x4

677.87 =∑ [(Coupon rate*1000/400)/(1 + 11/400)^k]     +   1000/(1 + 11/400)^20x4

k=1

Coupon rate% = 7