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Default Formula to calculate someone's exact age

I tried using (for example) "=YEAR(D6)-YEAR(E6)" to determine someone's exact
age based on their birthdate and today's date (formatted military-style as
dd-mmm-yy). In the example below, the above formula produces an incorrect
answer because it seems to round up.
Subtracting the following two dates YEAR(28-Aug-07)-YEAR(17-Sep-83) produces
the number "24", which is correct when you go by the year "yy", but actually
incorrect because this person isn't actually 24 years old until 17-Sep-07.
Why does EXCEL seem to round up?

 
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