Assuming the market is arbitragefree if a sixmonth pure disc

Assuming the market is arbitrage-free, if a six-month pure discount bond yields 1.9%, a one-year pure discount bond yield 2.3%, an eighteen-month pure discount bond yields 2.65%, and a two-year discount bond yields 3.05%, what should be the price of a two-year $1,000 6% par-value bond with semiannual coupons?

Solution

Interest = 1000 x 6% = 60

The bond is with semi annual coupons, we can either take the rates and divide them by 2 and take 4 periods or we can use the annual rates and take 2 periods instead.

Price of the bond = Present value of future cashlows discounted @ yield which is 3.05%

so, price of bond = 60 / (1.0305)^1 + 60 / (1.0305)^2 + 1060 / (1.0305)^3

                            = $1083.364