SQL help - date sensitive price retrieval

[Gerald Novak]

Wierd.
If I do the following, I get the right date:

Select max(My_date) from Mytable
where MY_ID = 'A'
and My_date < '1988-27-04')

However if my data looks like this:
MY_ID MY_DATE PRICE
A 3/6/1987 12:00:00 AM 1
A 4/1/1988 12:00:00 AM 2
A 4/28/1989 12:00:00 AM 3
B 3/6/1987 12:00:00 AM 5
B 4/1/1988 12:00:00 AM 6

and I query using:
Select max(My_date), PRICE from Mytable
where MY_ID = 'A'
and My_date < '1988-27-04')

I get the right date (4/1/88) but get the first price (1)
How do I query to get the price corresponding to the date retrieved?