Can I try? I'm more of a Math Ditz than a Math Whiz so my answer may be way off the mark but here goes nothing:
The answer is 500 bananas.
Starting at Point A, each Point thereafter is a 250 mile mark (B, C, D then E is the market)
Point A - Take 1000 bananas to Point B. 250 eaten, 250 to go back, leave 500 there. Go back.
Point A - Take 1000 bananas to Point B. 250 eaten, 250 to go back, leave 500 there. Go back.
Point A - Take the last 1000 bananas to Point B. 250 eaten, 750 left.
You now have 1750 bananas at Point B
Point B - Take 1000 bananas to Point C. 250 eaten, 250 to go back, leave 500 there. Go back.
Point B - Take the remaining 750 bananas to Point C. 250 eaten, 500 left.
You now have 1000 bananas at Point C
Point C - Take 1000 bananas to Point D. 250 eaten.
You have 750 bananas at Point D
Point D - Take 750 bananas to Point E (the market). 250 eaten.
You have 500 bananas to sell at the market
No?
Sorry, I can't do those calculations, it would make my head explode

.
Is this wrong? Please tell me what my mistake is.
Thanks!
Sorry, had to edit cause I missed a point!