value of the forward contract on the equity index

CFA Level II Derivatives
#1

While calculating value of the forward contract on the equity index (continuous dividends), why is the spot price at time t discounted at the dividend yield? Isn’t valuing the PV of future dividends possible in continuous dividends and then deduct this figure from the spot price?

Thanks in advance for your help.

#2

Yes you can do that. Note that S0 * e^rate * e^-yield is approximately equal to:

S0 * e^rate - S0*yield