Find exact or nearst lower correspoding value in a lookup table

Unfortunately I can't seem to post attachments here so here's what data I have:

On tab [Amount]

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On tab [source]

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Based on what I fill in in column Amount.1, my formula does a lookup in column source.A, and finds the corresponding value in source.B and shows that in column Amount.2
This formula works:

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However, it finds the closest value in source.A, even if that value is HIGHER than the value I enter in Amount.1
So for example, when I enter "111.20" in Amount.1, it now shows "41.67", but the value I want is the value that corresponds to either exactly 111.20 OR the nearest lower value. In this case 111.20 does not exist, so it should take the value 108 and thus return corresponding value "40.00"

Fast answers need visual help. Please read the yellow banner at the top of this page on how to attach a file.

Try this
Sheet1!A2=111.20

=INDEX(source!$B$2:$B$1961,MATCH(Sheet1!A2,source!$A$2:$A$1961,1))

Try =VLOOKUP(Amount!B4,source!$A$2:$B$1961,2,TRUE)

Function is given in Column C. Pl see file.