Question

Union Local School District has a bond outstanding with a coupon rate of 2.8 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.4 percent, and the bond has a par value of $5,000. What is the price of the bond

Answer 1

Answer:

The price of the bond is $4,632.16

Explanation:

Coupon payment = $5,000 x 2.8% = $140 /2 = $70 semiannually

Number of period = n = 16 years x 2 period per year = 32 period

Yield to maturity = 3.4% annually = 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 =$70 x [ ( 1 - ( 1 + 1.7% )^-32 ) / 1.7% ] + [ $5,000 / ( 1 + 1.7% )^32 ]

Price of the Bond = $70 x [ ( 1 - ( 1.017 )^-32 ) / 0.017 ] + [ $1,000 / ( 1.017 )^32 ]

Price of the Bond = $1,716.72 + $2,915.41

Price of the Bond = $4,632.13