Question

Mr. Simpson buys a $1000 semi-annual coupon bond paying interest at 6.8%/year compounded semi-annually and redeemable at par in 12 years. Mr. Simpson's desired yield rate is 9.8%/year compounded semi-annually. How much did he pay for the bond?

Answer 1

Price paid for bond wil be present value of cash future Cash Flows that is coupon and face value at end.

face value =   1000
Years remaining to Maturity =   12
Semiannual periods (n)= (12*2) =   24
Coupon rate =   6.80%
Semiannual Coupon = 1000*6.8%/2 =   34
YTM =    9.80%
Semiannual yield (i) = 9.8%/2=   0.049

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n  
=34*(1-(1/(1+0.049)^24))/0.049 + 1000/(1+0.049)^24  
=790.9919132  

So he will pay $790.99 for the bond