The US mint never made any such coin. It is a privately made coin. The value will simply depend on what the coin was symbolizing and what a dealer is willing to pay.
Lincoln, Wheat Ear Reverse (Wheat Penny's) cents were struck from 1909 to 1958. A 1888 penny is a Indian Head cent with an average value of $1.00-$3.00 for most coins. NOTE: The wreath on the reverse is Oak not Wheat.
the penny post was invented in 1888
in 1888
The last Liberty head (a/k/a/ "Large") cents were made in 1857. All cents dated 1888 are Indian Head cents. Please see the Related Question for more information.
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A 1888 small cent coin is valued: Good condition-$1.50, Fine condition-$4.00, Uncirculated-$40.00 Proof-$160.00 There is also some 1888 small cent coins that were minted 1888 with the last 8 spamped over a seven and these are more valuable: Very Good condition-$650.00, Fine condition-$1,000.00, Uncirculated-$8,000.00.
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Most years of issue of the British Queen Victoria Penny could be described as a "Passion Penny", some more so than others. The title "Passion Penny" arises from the proximity and angle of the shaft of the trident she is holding in relation to her groin. The humour of the "Passion Penny" design must have worn thin after 50 odd years, and from 1895 the trident shaft was moved away from the groin, almost to the knee. For a valuation of a British Penny, or any other coin, please specify the year.
This is not enough information to give an accurate value amount. Need to know 'Type' of penny, 'Date' of penny and 'condition' of penny.
1888 makes it an Indian head cent, which is a small coin (same size as modern Lincoln cents). The '88 is a relatively common date, worth anywhere between $2 and $50 depending on condition. If the coin is in fact larger, still dated 1888, then that's probably not Liberty on the coin, but rather Queen Victoria. If it is, the denomination will say "One Penny" rather than "One Cent". Prices for that coin start at around $3.