Question: Why does Joseph Smith state in his 1832 First Vision account that he was in his "16th year" of age?

Pearl of Great Price Central, Joseph Smith - History Insight #8: How Old was Joseph Smith at the Time of the First Vision?

The only account showing a different age is the 1832 account, which states age 15 rather than 14

In the 1832 account, Frederick G. Williams inserted the "in the 16th year of my age" above Joseph's text after Joseph had already written it. (See: "History, circa Summer 1832," The Joseph Smith Papers)

Joseph's 1832 account states the "16th year" of his age in the handwriting of Frederick G. Williams

In Joseph Smith's 1832 First Vision recital he said that he was "in the 16th year of [his] age" when the manifestation took place but in all other accounts in which he mentions his age, he was in his "fifteenth year."

Is this evidence that the Prophet's story evolved over time, and was thus a fabrication to begin with?

The only First Vision account that provided a different age was the 1832 account written in Joseph Smith's own handwriting. In 1832, 12 years after the First Vision, Joseph wrote, "we were deprived of the bennifit of an education suffice it to say I was mearly instructid in reading and writing and the ground rules of Arithmatic which constuted my whole literary acquirements."

There is nothing nefarious in Joseph Smith correcting his own slight mathematical miscalculations

Although the portion of Joseph's 1832 history is in his own handwriting, the text insertion of "in the 16th year of my age" was in the handwriting of Frederick G. Williams, Joseph's scribe. It is likely that Joseph's dating schemes were slightly off when he dictated his age to Williams, many years after-the-fact. There is nothing nefarious in Joseph Smith correcting his own slight mathematical miscalculations.

Two years later, Oliver Cowdery had Joseph's 1832 history in his possession when he began publishing history of the Church in late 1834 in the Latter-day Saints' Messenger and Advocate. Oliver clearly established Joseph's age as 14 ("the 15th year of his life") during the period of religious excitement (although Oliver ultimately never described the actual First Vision at this time). Once the date of the First Vision was correctly established it remained steady throughout all subsequent recitals as the "15th year" or "age 14."

Notes

Question: Why does Joseph Smith state in his 1832 First Vision account that he was in his "16th year" of age?