Using MATCH and INDEX function with multiple criteria

We're selling language courses that have a different price depending on when a course is taken. We're trying to build a price quote application that needs to look up a certain school and course and price driven by a start date.

How can I build a lookup function that says: pick the price of school X and course Y when the start date falls between dd/mm/yyyy and dd/mm/yyyy?

I manage to build a look up function with MATCH and INDEX when the condition of start date is exactly matched but dont know how to instruct it to match a value between a start and end date.

I have attached the simplified setup and appreciate anyone's help!