Problems combining IF and MAX to get the right result

Hi, I was wondering if anyone could help. Its a tricky question to ask - so I am hoping the answer is more straightforward than the wording of the question! OK Imagine the following table

Fruit Date Price New Date
Apple 01/01/00 1
Apple 02/02/00 2
Banana 03/03/00 1
Banana 04/04/00 2
Pear 05/05/00 1
Pear 06/06/00 2

WHat I would like to appear in the New date column is the date that each fruit was at its most expensive, so the table would become:

Fruit Date Price New Date
Apple 01/01/00 1 02/02/00
Apple 02/02/00 2 02/02/00
Banana 03/03/00 1 04/04/00
Banana 04/04/00 2 04/04/00
Pear 05/05/00 1 06/06/00
Pear 06/06/00 2 06/06/00

Is there a formula that would provide me with the outcome above.

Many thanks for your help,

Paul