A $1,000 face value bond matures in 11 years, pays interest semiannually, and ha

Question

A $1,000 face value bond matures in 11 years, pays interest semiannually, and has a 6.5 percent coupon. The bond currently sells for $1,025. What is the yield to maturity?

A. 6.17 percent

B. 6.18 percent

C. 6.28 percent

D. 6.34 percent

E. 6.37 percent

Last year, BT Motors issued 10-year bonds with a 9 percent coupon and semi-annual interest payments. What is the market price of a $1,000 bond if the yield to maturity is 8.9 percent?

A. $1,003.97

B. $1,006.53

C. $1,042.89
D. $1,414.14

E. $1,585.36

Explanation / Answer

1.

Pv is 1025

Coupon payment is 6.5%annual =$ 65annual or 32.5 semiannual

Time us 11years or 22 semiannual time period

Using the pv of annuity

1025=32.5[(1-(1+r/2)^-22)/r/2]+1000(1+r/2)^-22

Here r is ytm

Here we can find the value of r either by trial and error or with the help of financial calculator

By putting the different value given in equation we find out that ytm is option B that is 6.18%.

1025=32.5[(1-(1+.0618/2)^-22)/.0618/2]+ 1000 (1+.0618/2)^-22

1025=32.5(15.7942)+1000(.51196)

1025=513+512

1025=1025

2.

Here Coupon payment is $45 semiannual

Time is 20 semiannual periods

Ytm is 8.9% semiannual or 4.45%semiannual

Again using the pv of annuity formula

Pv= 45[(1-(1+.089/2)^-20)/.089/2]+1000(1+.089/2)^-20

=45(13.0645)+1000(.4186)

=587.90+418.63

=1006.53

So option B is correct

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