Simple answer: 10 cents. Why? 1965 and later dimes are made of cupronickel clad metal and has no precious metal or design value.
Specifically, the reference "liberty dime" does necessarily refer to one specific dime design. ALL American dimes have the word LIBERTY on them so that's not a distinguishing feature. What does distinguish a dime is their design, either that of the draped or capped bust, the seated liberty, the winged liberty head, and of course the Dismes which were never circulated. All dimes bear the word liberty.
Dimes pre 1965 have varying values and also bear the word Liberty. Those minted after and starting 1965 which are made of clad and have only a "present day" value; or 10 cents. Further, the latter are usually referred to as "Roosevelt dimes" because they show a picture of President Franklin Roosevelt.
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The value of a 1842 seated liberty dime is about $20 in G-4(good) condition.
The Liberty dime minted in 1943 was 90% silver. The current rate for a circulated 1943 Liberty Dime is the current value of the silver of the coin, presently $5.50
A 1918 Dime - aka - Winged Liberty/Mercury Dime - is worth in good condition (G4): $4; if its mint state is MS60, the value is: $70.
All US dimes have the word LIBERTY on them. A 1960 dime is a Roosevelt dime and all are very common. As of 8-27-11, if it has any wear the value is for the silver, about $3.00.
A '44 Mercury dime is worth about $2.50.