The dual dates seen on the front of any of the Presidential Dollars are the years served in office. The issue dates (2010 for this one) and mintmarks are on the edge of the coins. None of the coins are made from GOLD! They are made of brass. Any of the coins found in circulation are only face value.
Look on the back of the coin to see if there's a small mint mark letter. It may be blank or there may be an O or S.
Numismedia lists the following approximate retail values as of 04/2010:
No mint mark (Philadelphia):
Very worn condition - $28
Moderately worn - $52
Slightly worn - $71
Almost no wear - $249
Uncirculated - $570 to $12,190 depending on quality
"O" mint mark (New Orleans):
Very worn condition - $32
Moderately worn - $54
Slightly worn - $69
Almost no wear - $272
Uncirculated - $540 to $14,060
"S" mint mark (San Francisco):
Very worn condition - $52
Moderately worn - $150
Slightly worn - $360
Almost no wear - $1,626
Uncirculated - $4,200 to $10,630
Retail is $200 to $600 depending on condition.
One dollar
The Buchanan dollar was minted in 2010, and is worth exactly one dollar.
$1. It is not gold, and was not made in 1801. It is a modern coin worth only the face value.
Only proof and collectors coins sold from the Mint have more than face value. Remember, the coins are made of brass, not gold. It's a dollar spend it.
Only $1 unless in mint packaging. The coins are in common circulation and worth no more than face value.
These are general issue coins. An uncirculated one might sell for $2 at a coin shop. One that you get in your change is worth $1.
This coin would have to be seen before an accurate estimate of value could be made.
The James Garfield dollar coin was minted in 2011, and is worth exactly one dollar.
Take it to a local coin collector.
There's no US coin called an "old buck coin". What you have is a modern Presidential dollar worth face value only. The dates 1857-1861 are the years that James Buchanan served in office. The minting date 2010 is on the coin's edge.
1 dollar
Face value.
It's worth exactly one dollar (and it's made of brass, not gold).