Question

The US Treasury issued a 10-year bond with an annual coupon of 5% (face value 100). What is its price if the market requires a yield-to-maturity of 5%? What is its price if its coupon is paid semi-annually? Please show your work.

Answer 1

Face Value of bond = $1000

a). Annual Coupon Bond = $1000*5%

= $50

No of years to maturity(n) = 10 years

YTM = 5%

Calculating the Price of Bond:-

Price = $386.085 + $613.913

Price of Bond = $1000

So, its price if the market requires a yield-to-maturity of 5% is $1000

b). Now, coupon are paid semi-annually.

Semi-Annual Coupon Bond = $1000*5%*1/2

= $25

n = 10 years*2

= 20

Semi-annual YTM = 5%/2

= 2.5%

Calculating the Price of Bond:-

Price = $389.73 + $610.27

Price of Bond = $1000

So, price of bond if coupons are paid semi-annualy is $1000

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