star trek - How old was Peter Preston when he entered Starfleet Academy?

In Star Trek II: The Wrath of Khan Admiral Kirk inspecting the Enterprise briefly talks to a young looking person.

KIRK: Ah. And who do we have here?

PRESTON: Midshipman First Class Peter Preston, engineers mate, sir!

KIRK: First training voyage, Mister Preston?

PRESTON: Yes sir!

http://www.chakoteya.net/movies/movie2.html1

And some versions of the movie have Mr. Scott add that Preston is his sister's youngest child.

When I first saw Star Trek II: The Wrath of Khan I was rather shocked by how small and thus young Preston looked. Since Starfleet is usually more or less based on the modern US Navy and Preston looked too young for the US Navy I thought he should have been too young for Starfleet.

Then I recognized Peter Preston's actor as Ike Eisenmann and did a little "age computation" to deduce that if Preston was as old as Eisenmann he would have been about 18 and old enough to Starfleet. At the present time the minimum age to enter US service academies or enlist in the armed forces is 17. Of course I still thought that Preston looked a bit short and small to enlist or to enter the Academy, but maybe Starfleet, with its push button warfare style, doesn't need officers or men to be as big and strong as modern armed services do.

Valorum's answer to this question: Is it possible to enroll in Starfleet Academy as an adult?2

begins by saying:

There appears to be no minimum or maximum age at which one can enrol in Starfleet Academy. At the lower end, we see Wesley Crusher and Peter Preston entering the Academy at a very young age (15 and 13 respectively) whereas Garak (who seems to be in his 40's) nearly fools Worf into helping him to apply.

Wesley Crusher takes a highly competitive test to enter Starfleet Academy in "Coming of Age" and he does not get the only open slot at the Academy. I have always figured that they were being tested for a special program that could admit younger than usual persons to the Academy if they were very exceptionally talented, and that the Academy entrance standards were not usually that strict. I have wondered if other Star Trek characters like Spock, Alternate Universe Chekov, and Peter Preston also entered the Academy via that hypothetical special entrance program that might allow persons to enter at a younger age than usual.

In the "The Menagerie Part 1" Commodore Mendez said Captain Pike was injured rescuing cadets during a disaster.

MENDEZ: He went in bringing out all those kids that were still alive. Just wanted you gentlemen to be prepared.

http://www.chakoteya.net/StarTrek/16.htm3

When I first saw the episode I assumed that, like cadets in the 20th century armed forces, the cadets would all be 18 and older, older than me, so they hardly seemed like "kids" to me. But if Peter Preston could be in Starfleet age 14, then it is possible that many persons young enough for me to have considered them kids would have been killed and injured during the disaster.

Khan's followers who were killed aboard the Reliant in TWOK looked like they were mostly in their twenties, but Khan's followers in "Space Seed" should have been forty or fifty by then. Did Khan's followers in "Space Seed" look very young for their ages in TWOK? Were Khan's followers in TWOK the children of his followers in "Space Seed", aged under 15 but looking very mature for their ages? Were Khan's followers in TWOK augmented children who escaped from Earth in 1996 with Khan's adult followers?

And then there was the baby in Khan's group in early scripts, who presumably was vaporized in the Reliant.

We saw only a small sample of the presumably hundreds of cadets and trainees on the Enterprise in tWOK. If the youngest looking one, Peter Preston, was over 18, there would be no reason to believe than any of them were under 18. But if Peter Preston was only 14, some of the other cadets and trainees aboard the Enterprise could also have been that young, and possibly younger.

Thus it is certainly possible to imagine that the battles in TWOK could have been between two ships with a significant proportion of kids in their crews.

So my question is: How old was Peter Preston when he entered Starfleet Academy?

Is Valorum correct to say that Peter Preston was 13 when he entered Starfleet Academy? Was he some other age when he entered Stafleet Academy?