No you do not need a second passport to retire,

No you do not need a second passport to retire, work, or live abroad.  You can reside in Panama as a tourist but it is recommended to apply for one of the many visas offered.  There are plenty to choose from for the retired and non-retired.  Panama has opened its doors to many nations due to the need for skilled labour.  The new Friendly Nations visa has made it a lot easier for individuals who are not ready to retire but who want to live and work in Panama.
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