I am taking "Financial Engineering and Risk Management Part I" from Columbia University on coursera and I got a seemingly simple question wrong on the first quiz. This is all based on the no-arbitrage arguments. Here is the question:
During the lesson we constructed a portfolio to try to get the value of a forward at an intermediate time. Here is what we got:
What was missing at this point was how to get F(t) and F(0). A few slides back we did:
Ok so now I have all of the ingredients for this forward soup. I got the forward price at time zero with the stock price at time zero divided by the discount for the whole period (two 6 month periods so its squared). Then I got the forward price at 6 months by taking the price at 6 months and dividing it by the discount for one six month period. I took the difference between the two and multiplied it by the discount factor for six months (between t and T). I ended up rounding off to 27. What am I doing wrong? Below is a picture of my calculations (I did not round any intermediate calculations). I'm more of a pencil and paper guy but if you want I can type it all up.
Also, Happy New Year to you all!