Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 6.2%. Now, with 6 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is the price of the bond now

The price of the bond is $659.64.

Explanation:

C = coupon payment = $62.00 (Par Value * Coupon Rate)

n = number of years = 6

i = market rate, or required yield = 15 = 0.15 = 0.15 / 2 = 0.075

k = number of coupon payments in 1 year = 2

P = value at maturity, or par value = $1000

BOND PRICE = C/k [ 1 - (1 / (1 + i) ^nk) / i ] + [ P / (1 + i) ^nk) ]

BOND PRICE = 62/2 [ 1 - (1 / (1 + 0.075) ^6x2) / 0.075 ] + [ $1,000 / (1 + 0.075) ^6x2) ]

BOND PRICE = 31 [ 1 - (1 / (1.075) ^12) / 0.075 ] + [ $1,000 / (1.075) ^12) ]

BOND PRICE = 31 [ 1 - (1 / (1.075) ^12) / 0.075 ] + [ $1,000 / (1.075) ^12) ]

BOND PRICE = $239.79 + $419.85 = $659.64