Question

A 30-year maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 7.80%. (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places.) a. What is the yield to maturity if the bond is selling for $920? b. What is the yield to maturity if the bond is selling for $1,000? c. What is the yield to maturity if the bond is selling for $1,125?

Answer 1

a.Information provided:

Face value= future value= $1,000

Market price= present value= $920

Time= 30 years*2= 60 semi-annual periods

Coupon rate= 7.8%/2= 3.9%

Coupon payment= 0.039*1,000= $39

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -920

N= 60

PMT= 39

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.2720.

Therefore, the yield to maturity is 4.2720%*2= 8.5440%   8.544%.

b.Information provided:

Face value= future value= $1,000

Market price= present value= $1,000

Time= 30 years*2= 60 semi-annual periods

Coupon rate= 7.8%/2= 3.9%

Coupon payment= 0.039*1,000= $39

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -1,000

N= 60

PMT= 39

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.90.

Therefore, the yield to maturity is 3.90%*2= 7.80%.

c.Information provided:

Face value= future value= $1,000

Market price= present value= $1,125

Time= 30 years*2= 60 semi-annual periods

Coupon rate= 7.8%/2= 3.9%

Coupon payment= 0.039*1,000= $39

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -1,125

N= 60

PMT= 39

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.4081.

Therefore, the yield to maturity is 3.4081%*2= 6.8163% 6.816%.