Formula in E3:

=INDEX(A1:A10, MATCH(MIN(ABS(A1:A10-\$E\$1)), ABS(A1:A10-\$E\$1), 0))

How to enter an array formula

1. Select cell E3
2. Type or copy/paste above array formula to formula bar
3. Press and hold Ctrl + Shift
4. Press Enter

Download excel example file
find-nearest-date.xls
(Excel 97-2003 Workbook *.xls)

Functions:

INDEX(array,row_num,[column_num])
Returns a value or reference of the cell at the intersection of a particular row and column, in a given range

ABS(number)
Returns the absolute value of a number, a number without its sign.

MATCH(lookup_value;lookup_array; [match_type])
Returns the relative position of an item in an array that matches a specified value

MIN(number1,[number2])
Returns the smallest number in a set of values. Ignores logical values and text

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