Let S(t) = the price of some security at time t. Suppose S(0) = 80 and the effective yearly interest rate is r = .03.
You write a contract to purchase the security in 8 months. What price should you agree to purchase the security at?
Suppose at 3 months the price of the security has fallen to $ 70. What is the value/liability of the long position of the forward?
Suppose you wish to purchase the security in 15 months, (as above, given S(0) = 80 and r = .03) for $ 60 what should you pay for the contract today?
Suppose, in addition, the security pays 1 dividend of $ 5 at time t = 1 month. What should the exchange price be for a forward contract with maturity at 9 months?
Suppose the security pays continuous dividends at a rate of 6% (and no discrete dividends) in this case, what should the forward price be at 2 years?