Should an Officer who was non-selected for promotion, and discharged at 16 years of service, reenlist to finish their 20?

Absolutely, 4 years is nothing compaired to the 16 you've already served. Why would you give up a retirement check? (Reserve retirement may not pay the bills under the old system, but it is time served and money earned.)

The short answer would be yes. But what are your current circumstances? Are you disabled, reenlistment code, age etc. If you are receiving a VA disability and was accepted by a branch for reenlistment you would have to suspend your disability payments or your military pay, you cannot receive both. Are you thinking Active or Guard/Reserve, officer or enlisted? Way to many variables to give you a straight answer. My suggestion if you’re serious about pursuing this are contacting a recruiter and seeing what options you may have. Good luck!

Probably the least painful path is to sneak into the Reserves, and get your remaining good years of service and apply for a Reservist Retirement based on your accumulated points. I presume your 16 years are fully active so that's going to be 5840 points right there. Then......... you'd need 4 more good reserve years, and at minimum need 50 points each year, 15 of which are automatic, and 48 for attending monthly drill then at minimum 14 points for annual training. 77 being the "minimum" without missing anything (I've never had less than 90ish) So at a minimum you'll retire with 6040 points.

The 20 year CPT pay is $7543. 20 years will get one 50% of that base pay (the old retirement plan) which is based on 7300 points. So a reserve pension would be prorated, and in your worst case (50 points the remining 4 years) is [6040/7300] * 0.5 * 7543 = $3120 a month.

Do I have this correct folks?

Not completing out the remainder 4 years is at a minimum loss of $3120 a month for the rest of his life?

Short answer: yes. As I understand your profile, you are a Captain in the Reserve. If the question is not hypothetical, but is personal, you've been twice non-selected to major. Your profile shows you were previously an E-6. If you choose to enlist to complete your 20 good years, then you will probably come back in as an E-6.

My experience with officers going to enlisted to complete 20 is limited. I worked with a captain pilot who was twice passed over, but was allowed to remain on active duty as an O3 to 20 years because the Air Force was short on pilots. See if your MOS is critical. I also was a Scout Leader with an Air Force SSgt (E5) who had been a Captain. He sued the Air Force, the officers who wrote and endorsed his last few OERs before his promotion board. He won! He went to work one morning as a SSgt and came home that afternoon as a major. This is rare. I don't recall the exact grounds for his suit. It was not because he was discriminated against as a member of a protected class. It had something to do with supervision and geographical separation from his rater. There was an operations clerk at an Air Base where I worked who was a Master Sergeant, but wore Command Pilot wings. I asked about him and was told by my boss he had been a major who was twice passed over for lieutenant colonel. He chose to finish out his 20 as an enlister person then decided to stay even longer.

I think it's worth it financially. You'll probably retire as a Captain with 20 years of service. Good retirement pay. You'll be eligible for TRICARE till you're 65, then TRICARE for Life. Your retired ID card will get you installation access and use of AAFES, Commissary, Pharmacy, etc. It's well worth it.

I knew of a major passed over at 16 years during a major RIF. He chose to enlist as an NCO and served to 30 years. His commander called him a disgrace to the officer corps for doing so.

He also joined his State Reserve where his family had friends and in State government. This was back when they still had both Regular and Reserve officer promotion opportunities. So on all his available weekends and on leave he served with his State Guard and was promoted to Brigadier.

So on his last day of active duty service he pinned on his star and paid his former commander a visit. He had one terrified full colonel terrified up against a wall. It was beautiful.

I had a friend who was twice passed over for Major. He resigned his commission, put his stripes back on as an E-5, got promoted, reached 20 and retired as a Captain.

Absolutely! Your retirement pay would be at the highest rank you held, so what's four more years? I served with several people in the Reserves who were officers on active duty and got passed over, so they enlisted to finish out their time.

I was nonselected for Captain with 13 years. After 911, I enlisted in the Air Force served 3 years and transfer back into the Army to prepare for Chaplain. Was promoted to E6 and three months Direct Commission to Army Chaplain Captain 3 months later Disability Land. Prove you can continue serving your country to retirement regardless of the rank. Just keep your head up.

if allowed to do so, Absolutely .
Four Years will go with a Blink of a eye, it is nothing, by doing so, he and his family will receive a check of at least 50% of his highest 3 years, every month for the rest of his life. it like hitting the lottery and receiving X Number of dollars at the 1st of each month for the rest of his life.
people by lottery tickets for this and throw thousands of dollars away for a chance like this, funny all they had to do is stand up and protect and serve this great nation for 20 plus years :)

I did it. I had 17 good years and was in reserver status. It took a while. I enlisted as e-6. There was some sort of GO sign off needed for E7. After 6years I was able to re-commission and got back my captain. I got promoted to MAJ and ran out of time to make LTC. I Ended up with 32 good years. I don't recommend it for career path but I managed it.