Question

Assume a par value of $1,000. Caspian Sea plans to issue a 15.00 year, semi-annual pay bond that has a coupon rate of 7.85%. If the yield to maturity for the bond is 8.45%, what will the price of the bond be?

Answer 1

Par value = $1,000

Semi annual Coupon rate = 7.85%/2 = 3.925%

r = Yeild to maturity = 8.45%/2 = 4.225%

n = 15*2 = 30 semi annual

C = Semi annual coupon = Par Value * Semi annual Coupon rate = $1,000 * 3.925% = $39.25

Price of bond = [C * [1 - (1+r)^-n] / r] + [Par value / (1+r)^n]

= [$39.25 * [1 - (1+4.225%)^-30] / 4.225%] + [$1,000 / (1+4.225%)^30]

= [$39.25 * 0.711036568 / 0.04225] + [$1,000 / 3.4606455]

= $660.548764 + $288.963432

= $949.512196

price of bond today is $949.51