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.

Answer 1

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