January 20, 1961 .
JFK's inauguration was January 20, 1961
JFK half dollars were first issued in 1964. And 1963 is the last year for Franklin half dollars, plus the US Mint has never issued a gold JFK coin of any type. If the coin is a counter stamped, gold plated Kennedy half dollar it's only 50 cents.
Kennedy half dollars are not made of gold'
1917
The year was 1961.
1960
a lot.
1961-1963
It's likely a "Gold Charm" of some type, not a US Mint product.
January 20, 1961 - November 22, 1963
The Mint does NOT make gold half dollars. The coin has been gold plated. Gold plated Kennedy halves are only face value.