Question

Union Local School District has bonds outstanding with a coupon rate of 3.1 percent paid semiannually and 22 years to maturity. The yield to maturity on these bonds is 3.4 percent and the bonds have a par value of $10,000.
What is the price of the bonds?

Answer 1

Answer:

The price of the bond is $9,537.91

Explanation:

Coupon payment = $10,000 x 3.1 = $310 / 2  = $155

Number of period = n = 22 x 2 = 44 semiannual periods

Face Value = $10,000

Yield to maturity = 3.4% yearly = 3.4% /2 = 1.7% semiannually

Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond =$155 x [ ( 1 - ( 1 + 1.7% )^-44 ) / 1.7% ] + [ $10,000 / ( 1 + 1.7% )^44 ]

Price of the Bond = $155 x [ ( 1 - ( 1.017 )^-44 ) / 0.017 ] + [ $10,000 / ( 1.017 )^44 ]

Price of the Bond = $4,774.94 + $4,762.97

Price of the Bond = $9,537.91