Congratulations, Hana, you have a valuable coin. For one reason or another, I am not sure why, the old German Empire issued only a very few 50 pfennig coins between 1896 and 1903. These coins, then, are worth a strong premium over other 50 pfennigs of the era. They minted plenty of earlier 50 pfennigs, so dates before 1896 are not as valuable, as follows:
50 PFENNIG 1875 TO 1878
worn: $10 US dollars approximate catalog value
average circulated: $20
well preserved: $55
fully uncirculated: $100
50 pfennig dated 1875E and 1875H are more rare; multiply these values by 6
50 pfennig dated 1878E are quite rare; multiply these values by 10
50 PFENNIG 1896 TO 1903
worn: $150 US dollars approximate catalog value
average circulated: $250
well preserved: $400
fully uncirculated: $800
50 pfennig dated 1902F are worth 1.5 times the values quoted above: less than a hundred thousand of these coins were made!
These are inflated catalog values. See our Important Terminology page for more info about catalog values.
Look at the coin in the picture. It is from Stephan Knopik and is currently selling retail for $680 US dollars. It is worth every penny because the coin is in a superb state of preservation.
NEVER CLEAN A COIN. CLEANING RUINS VALUE.
The thing that will make a difference with your coin is its state of preservation. You give 'average circulated' as an assessment of grade for your piece, so I think your coin would sell on the retail market for about $400. Stephan's coin pictured is in better shape than 'average circulated.'
Remember, coin dealers pay less than retail for coins they buy from the general public, so a dealer might pay you $300 for your coin (or thereabouts), figuring to make $100 gain when selling. The $100 goes to keeping the dealer's business alive.
If you have a coin worn completely down to a frazzle, it will only be worth the silver content of the coin, which is currently about $2 US Dollars. Look up the price of silver on a website like kitco.com, and multiply it by the amount of silver in the coin - 0.0804 troy ounces. The price of silver fluctuates from day to day.
Finally, with all valuable coins, you must consider the possibility of counterfeit. If you bought your coin on eBay within the past few years, it is possible that it is a fake. There are unscrupulous coin dealers everywhere, and eBay has a good dose of them. Fakes can be detected by knowledgable dealers and collectors, and some third party companies specialize in authenticating rare coins.
CoinQuest thanks MA-Shops Stephan Knopik for use of their coin image.