Question

Suppose you are reviewing a bond that has a 10% coupon rate paid semi-annually and a face value of $1,000. There are 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond?

Answer 1

Bond price = C x [1 – (1+r)-n/r] + F/(1+r) n

F = Face value = $ 1,000

C = Periodic coupon payment = Face value x Coupon rate/Annual coupon frequency

                                                = $ 1,000 x 0.1/2 = $ 1,000 x 0.05 = $ 50

r = Rate of return = 0.08/2 = 0.04 semi-annually

n = Number of periods to maturity = 20 x 2 = 40 periods

Bond price = $ 50 x [1 – (1+0.04)-40]/0.04] + $ 1,000/ (1+0.04) 40

                  = $ 50 x [1 – (1.04)-40]/0.04] + $ 1,000 x (1.04) - 40

                    = $ 50 x [(1 – 0.208289044662941)]/0.04 + $ 1,000 x 0.208289044662941

                    = $ 50 x (0.791710955337059/0.04) + $ 208.289044662941

                    = $ 50 x 19.7927738834265 + $ 208.289044662941

                    = $ 989.638694171324 + $ 208.289044662941

                    = $ 1,197.927738834260 or $ 1,197.93

Price of the bond is $ 1,197.93