Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 9% annual coupon. Bond L matures in 20 years, while Bond S matures in 1 year.

Assume that only one more interest payment is to be made on Bond S at its maturity and that 20 more payments are to be made on Bond L.

1. What will the value of the Bond L be if the going interest rate is 6%? Round your answer to the nearest cent.
   $   
   
   What will the value of the Bond S be if the going interest rate is 6%? Round your answer to the nearest cent.
   $   
   
   What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent.
   $   
   
   What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent.
   $   
   
   What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent.
   $   
   
   What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent.

Answer 1

a. if the going interest rate is 6%

Price of Bond S

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =20

interest rate (i) 6%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+6%)^20))/6%) + (1000/(1+6%)^20)

=1344.097637

So bond S price is $1344.10

Price of Bond L

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =1

interest rate (i) 6%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+6%)^1))/6%) + (1000/(1+6%)^1)

=1028.301887

So bond L price is $1028.30

b. if the going interest rate is 8%

Price of Bond S

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =20

interest rate (i) 8%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+8%)^20))/8%) + (1000/(1+8%)^20)

=1098.181474

So bond S price is $1098.18

Price of Bond L

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =1

interest rate (i) 8%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+8%)^1))/8%) + (1000/(1+8%)^1)

=1009.259259

So bond L price is $1009.26

C. if the going interest rate is 14%

Price of Bond S

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =20

interest rate (i) 14%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+14%)^20))/14%) + (1000/(1+14%)^20)

=668.8434724

So bond S price is $668.84

Price of Bond L

face value =1000

annual coupon amout =1000*9% =90

years to maturity (n) =1

interest rate (i) 14%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(90*(1-(1/(1+14%)^1))/14%) + (1000/(1+14%)^1)

=956.1403509

So bond L price is $956.14