Formalize: Forward Contracts on Investment Assets with Known Yield
(n Dividend Dates)

How many shares of a stock do you need to buy at t = 0 such that you will end up having exactly one share of the stock at t = T, but without accumulating dividends? The stock will pay dividend n times at known dividend rates of q₁, q₂, ...q_n at t₁ < t₂ < ...< t_n <T.

The answer to the question is buy (1 - q₁) (1 - q₂) . . . (1 - q_n) shares at t = 0.

Note:

1. The cost of obtaining a share of the stock that pays S_T at t = T is:
   S₀ (1 - q₁) (1 - q₂) . . . (1 - q_n)
2. Therefore, F₀ = S₀ (1 - q₁) (1 - q₂) . . . (1 - q_n)(1+r)^T  - - - (discrete compounding)

                           F₀ = S₀ (1 - q₁) (1 - q₂) . . . (1 - q_n)e^rT  - - - (continuously compounding)

Note: If you need further assistance in understanding this concept, view the Forward Contract on Assets with Continuous Known Yield video by clicking on the Instructional Videos link in the left menu.