Question was answered well by @Ezy, thanks for his help! Full answer in the comments below my question
This seems to be a basic question, but mysteriously unsolvable as far as I can see.
It concerns calculating the interest rate from a given stock futures price. It seems astonishingly hard to do.
Assume the following are given:
F - the Futures price
S - the Spot price
T - the Time to the futures expiry (days / 365)
D - the expected Dividend
t - the Time from the dividend ex-date to expiry
r - the Rate used
To keep it simple, assume there is only 1 expected dividend. Then the formula for the futures price is:
F = Se^(rT) - De^(-rt)
Then assume we have all the values except r. We know what F, S, T, t, and D are; and we want to solve for r.
I was unable to solve for r. (Perhaps my algebra is too weak). Wolfram Alpha professional also can't resolve a general 'r' from this equation either. If taken over the real numbers, then Wolfram Alpha can approximate r if all the other values are given. It looks like this is done through some kind of Goal-Seek or numerical analysis.
Why is this simple effort of getting r turning out to be so mysteriously difficult?
The final answer from @Ezy shows that the right answer is: F = Se^[(Rp-Rr)*T] - De^[(Rp-Rr)*t]