Find earliest date given a >= threshold

Maybe this

=MIN(IF(B2:B24>=E1,A2:A24))

Format as date

...confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer. Press F2 on that cell and try again.

Here, try this:

Formula:

=INDEX(A2:A100,MATCH(TRUE,INDEX(B2:B100>=E1,,),0))

cblindsey,
just to explain: mine and AlKey's formula will return same result as long as dates are in ascending order.

But in this case:

Date	 Price 
10.01.02	 $39,00 
10.02.02	 $40,94 
10.03.02	 $40,43 
10.04.02	 $39,81 
10.07.02	 $39,60 
01.01.14	 $42,00 
10.09.02	 $37,60 
10.10.02	 $38,94 
10.11.02	 $40,03 
10.14.02	 $39,93 
10.15.02	 $41,88 
10.16.02	 $41,30 
10.17.02	 $42,35 
10.18.02	 $42,35

Mine will return blue result (because it's first date that match criteria) and AlKey's will return red (because it's minimum date that match criteria).

Use formula that you rater want to return as result in case date's are mixed.