Originally Posted by

**brandond**
You solved for r correct? I have r~.0706.

I solve these by using PCP myself. I know I want to create synthetic bond maturing at 10000 at time .25. So, today, I must invest 9825.05. Using PCP, I set it up as such:

C-P-40e^(-.05*.25)=-40e^(-.0706*.25)

The minus sign on the right hand side tells me I am investing, which is what we do when purchasing a bond. So, I need 40e^(-.0706*.25)*X=9825.05 to replicate the purchase of the bond. Therefore X=250.

Now the trick is to realize that the prepaid forward on the stock is 40e^(-.02*.25), and we multiply the equation through by 250, so 250*40e^(-.02*.25) = 9950.1248, but each share only costs 40, so we divide by 40 to get the correct solution.

I probably would have got this wrong on the exam, I would have made the mistake of simply choosing 250.