Question

What is the value of a bond that has an annual coupon of 12%, a maturity of 5 years and the market yield is currently at 8%?

What is the value of a bond that has an annual coupon of 7%, a maturity of 10 years and the market yield is currently at 8%?

What is the value of a bond that has an annual coupon of 8%, a maturity of 15 years and the market yield is currently at 8%?

What is the value of a bond that has an annual coupon of 9%, a maturity of 20 years and the market yield is currently at 8%?

What is the interest on a $1,000 zero coupon bond with a yield of 6.75% for 2 years?

What is the yield of a $1,000 zero coupon bond maturing in 3 years purchased at $834.887?

Answer 1

1.Value of a bond that has an annual coupon of 12%, a maturity of 5 years and the market yield is currently at 8%

Face value(FV)= 1000

Annual Coupon pmt.= 1000*12%= 120

Market interest rate=Yield=r= 8%

No.of years to maturity =n= 5

Using the formula to find the value of the bond,

ie. PV of all its future coupon payments+PV of the Face value to be recd. At maturity --both discounted at the market yield.

ie. Value=(Pmt.*(1-(1+r)^-n/r)+(FV/(1+r)^n)

ie .Value=(120*(1-1.08^-5)/0.08)+(1000/1.08^5)=

1159.71

2.Value of a bond that has an annual coupon of 7%, a maturity of 10 years and the market yield is currently at 8%

Face value(FV)= 1000

Annual Coupon pmt.= 1000*7%= 70

Market interest rate=Yield=r= 8%

No.of years to maturity =n= 10

Using the formula to find the value of the bond,

ie. PV of all its future coupon payments+PV of the Face value to be recd. At maturity --both discounted at the market yield.

ie. Value=(Pmt.*(1-(1+r)^-n/r)+(FV/(1+r)^n)

ie .Value=(70*(1-1.08^-10)/0.08)+(1000/1.08^10)=

932.90

3.Value of a bond that has an annual coupon of 8%, a maturity of 15 years and the market yield is currently at 8%

Face value(FV)= 1000

Annual Coupon pmt.= 1000*8%= 80

Market interest rate=Yield=r= 8%

No.of years to maturity =n= 15

Using the formula to find the value of the bond,

ie. PV of all its future coupon payments+PV of the Face value to be recd. At maturity --both discounted at the market yield.

ie. Value=(Pmt.*(1-(1+r)^-n/r)+(FV/(1+r)^n)

ie .Value=(80*(1-1.08^-15)/0.08)+(1000/1.08^15)=

1000

4.Value of a bond that has an annual coupon of 9%, a maturity of 20 years and the market yield is currently at 8%

Face value(FV)= 1000

Annual Coupon pmt.= 1000*9%= 90

Market interest rate=Yield=r= 8%

No.of years to maturity =n= 20

Using the formula to find the value of the bond,

ie. PV of all its future coupon payments+PV of the Face value to be recd. At maturity --both discounted at the market yield.

ie. Value=(Pmt.*(1-(1+r)^-n/r)+(FV/(1+r)^n)

ie .Value=(90*(1-1.08^-20)/0.08)+(1000/1.08^20)=

1098.18

5.Interest or PV on a $1,000 zero coupon bond with a yield of 6.75% for 2 years

PV of Zero=FV/(1+Yield)^n

ie.1000/(1+0.0675)^2=

877.53

6.Yield of a $1,000 zero coupon bond maturing in 3 years purchased at $834.88

PV of Zero=FV/(1+Yield)^n

ie.834.88=1000/(1+Yield)^3

Solving the above , we get the Yield as

6.20%