Wow William, what a cool coin!
Worn, stained, and with a tainted eye appeal, your coin won't be worth much. I would keep it though!
Panama has been minting coins like this since 1935 all the way to 2008. Only the early coins are valuable, as not very many were minted. They made 200,000 each in 1935 and 1937. This gives these coins a decent collectible value today. Other dates after 1937 are worth very little.
The 'VRRACA' inscription refers to none other than Urracá, the Panamanian folk hero who fought the Spanish conquistadors in the first half of the 16th century. He looks like he means business!
These are the approximate values that the catalogs report for these coins.
1 CENTESIMO 1935 to 1937:
worn: $1 US dollar approximate catalog value
average circulated: $6
well preserved: $15
fully uncirculated: $35
The 1935 date is slightly less common and worth around 25% more than the values above.
1 CENTESIMO after 1937:
worn: less than $1 US dollar approximate catalog value
average circulated: less than $1
well preserved: less than $1
fully uncirculated: $3
Remember that these are inflated catalog values (read the Important Terminology page on the top left) and only apply to coins free of any problems like scratches, stains or spots.
The coin in our picture is being sold for $10.75 by Coin House Sesam Basel. This is a dealer selling coins for a profit. Their coin lies somewhere between 'average circulated' and 'well preserved' in state of preservation, but it has a spot around Urracá's eye, which lowers the eye appeal. If the spot weren't there, the value would improve by several dollars.
If you wanted to sell a coin like this to a dealer, he or she would likely pay you around $5. This is the margin of mark-up necessary to keep a business afloat.