Question

a. Consider a coupon bond that pays interest of $60 annually, has a par value of $1,000, matures in 2 years, and is selling today at a price of $1000. What is the yield to maturity on this bond?

b. Consider a zero-coupon bond with a par value of $1,000 that costs $500 and matures in ten years. What is the yield to maturity on this bond? Give the formula, and solve.

c. For the bond in part (b) above, what will be the price one year from today, if interest rates stay the same?

Answer 1

(a )Yield to maturity(YTM)= {Coupon+(face value-price)/years to maturity}/(Face value+Price)/2

Coupon=C , face value=F , price=P , years to maturity=n

i.e YTM= {C+(F-P)/n}/(F+P)/2

YTM={$ 60+($1000-$1000)/2 years}/($1000+$1000)/2

YTM=($ 60+0)/$1000=0.06=6%

(b )Formula for yield to maturity in case of zero coupon bonds is as follows:

Yield to maturity(YTM)= {(face value /present value)^1/number of years to maturity}-1

YTM=(F/P)^1/n-1

YTM=($1000/$500)^1/10-1

YTM=7.177 %

( c )For the zero coupon bond the price of the bonds one year from now = $ 500

Let X= Price of bond one year from now

Par value of the bond=$1000

Interest rate=7.177%

Therefore X= $1000/(1+0.07177)^9=535.90

i.e Price of bond one year from now=$ 535.90