Roadside Markets has 8.45 percent coupon bonds outstanding that mature in 10 years. The bonds pay interest semiannually. What is the market price per bond if the face value is $1,000 and the yield to maturity is 7.2 percent?

Market price of bond is 1,088.03

Explanation:

Price of bond is the present value of all future cash flows, Present value of all of all coupon payments and face value is calculated and added together to find the value of the bond.

As the interest is paid semiannually the calculations are made accordingly.

Coupon payment = 1000 x 8.45% = $84.5 annually = $42.25 semiannually

Number of periods = n = 10 years x 2 = 20 periods

Yield to maturity = 7.2% annually = 3.6% semiannually

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 = $42.25 x [ (1 - (1 + 3.6%) ^-20) / 3.6% ] + [ $1,000 / (1 + 3.6%) ^20 ]

Price of the Bond = $42.25 x [ (1 - (1.036) ^-20) / 0.036 ] + [ $1,000 / (1.036) ^20 ]

Price of the Bond = $42.25 x [ (1 - (1.036) ^-20) / 0.036 ] + [ $1,000 / (1.036) ^20 ]

Price of the Bond = $595.08 + 492.95 = 1,088.03