Question

A broker specializing in bonds has offered you $100,000 bond with a 10 year maturity and a 10% semi annual coupon at an 8% yield to maturity what is the price of the bond?

Answer 1

Bond Price Formula = Coupon Rate x Face Value of The Bond x {1-[(1+R)^-n]/R} + Face Value of The bond/(1+R)^n

where N is the no. of Periods

To calculate no. of Period = No. of Coupon Payments in a year X Life of Bond (which is 10 years given)

No. of Periods = 2 * 10 = 20 Periods

C = Semi Annual Coupon Rate

Now given that bond pays Coupons semi annualy,

therefore Annual Coupn Rate= 10 %. Semi Annual Coupon = Annual Copon Rate / 2 = 5%

and R = Semiannual YTM

Given that Annual YTM - 8%, therefore Semi annual YTM = 8% /2 = 4%

Therefore Price of Bond = 5% * $100000 {[1-(1.04)^-20]/0.04} + 100000/ (1.04)^20

Therefore Price of Bond = 5000 * 13.59 + 45639

Price of Bond = $ 113590.326