Question

a 20000 par value bond matures on january 1, 2020. The bond pays coupons at the annual rate of 7%, payable semiannually. The nomial annual yield to maturity is 10% compounded semiannually. Find the price of the bond on August 25, 2005.

Answer 1

The answer is $15,680.66.

Step-by-step explanation:

Semiannual coupon payment is 20,000 x 7% /2 = 700

* Present value of the bond as at 1st Jan 2006 is equal to:

+ Coupon payment at the time + Present value of 28 coupon payments in the next 14 years + Present value of face value repayment at the end of 14 years ( 14 x2 = 28 discounting periods) = 700 + (700/5%) x [1 - 1.05^(-28)] + 20,000/1.05^28 = $16,230.562

* We discount the present value of the bond as at 1st January 2006 to August 25 2005 to find the price of the bond ( from Aug 25 to 31st December there are 128 days, divided by 182.5 days for one period ).

16,230.562 / (1 + 5% x 128/182.5) = $15,680.66.

So the answer is $15,680.66.