Bond A has the following terms: Coupon rate of interest (paid annually): 12 perc
ID: 2616924 • Letter: B
Question
Bond A has the following terms:
Coupon rate of interest (paid annually): 12 percent
Principal: $1,000
Term to maturity: Ten years
Bond B has the following terms:
Coupon rate of interest (paid annually): 6 percent
Principal: $1,000
Term to maturity: Ten years
What should be the price of each bond if interest rate is 12 percent?
Price of bond A: $
Price of bond B: $
What will be the price of each bond if, after three years have elapsed, interest rate is 12 percent?
Price of bond A: $
Price of bond B: $
What will be the price of each bond if, after ten years have elapsed, interest rate is 10 percent?
Price of bond A: $
Price of bond B: $
Five years ago your grandfather purchased for you a 25-year $1,000 bond with a coupon rate of 10 percent. You now wish to sell the bond and read that yields are 7 percent. What price should you receive for the bond? Assume that the bond pays interest annually.
Explanation / Answer
What should be the price of each bond if interest rate is 12 percent?
Bond A:
Since coupon rate is equal to interest rate, price of bond A will be equal to the face value
Price of bond A = $1,000
Bond B:
Coupon payment = 0.06 * 1,000 = 60
Bond price = coupon payment * [ 1 - 1 / ( 1 + R)n ]] / r + face value/( 1 + r)n
Bond price = 60 * [ 1 - 1 / ( 1 + 0.12)10 ]] / 0.12 + 1,000 / ( 1 + 0.12)10
Bond price = 60 * 5.650223 + 321.973237
Bond price = 339.01338 + 321.973237
Bond price = $660.99
What will be the price of each bond if, after three years have elapsed, interest rate is 12 percent?
Bond A:
Price of the bond will remain $1,000 as the interest rate is equal to the coupon rate.
Bond B:
Number of periods = 10 - 3 = 7
Coupon payment = 0.06 * 1,000 = 60
Bond price = coupon payment * [ 1 - 1 / ( 1 + R)n ]] / r + face value/( 1 + r)n
Bond price = 60 * [ 1 - 1 / ( 1 + 0.12)7 ]] / 0.12 + 1,000 / ( 1 + 0.12)7
Bond price = 60 * 4.563757 + 452.349215
Bond price = 273.82542 + 452.349215
Bond price = $726.17
What will be the price of each bond if, after ten years have elapsed, interest rate is 10 percent?
Bond A:
At maturity the price of bond will be equal to the face value
Price of bond = $1,000
Bond B:
At maturity the price of bond will be equal to the face value
Price of bond = $1,000
Five years ago your grandfather purchased for you a 25-year $1,000 bond
Number of periods = 25 - 5 = 30
Coupon payment = 0.1 * 1,000 = 100
Price of bond = 100 * [ 1 - 1 / ( 1 + 0.07)20]] / 0.07 + 1,000 / ( 1 + 0.07)20
Price of bond = 100 * 10.594014 + 258.419003
Price of bond = $1,317.82