According to this Scroll article, more than two decades into his 49-year rule, Emperor Akbar, the third in the Mughal lineage, started focusing on things like religion, philosophy and the arts.
The emperor had an interest to have a look into the calendars of various faiths since he took interest in various religions and this led to him inventing, as Amartya Sen has said in his book The Argumentative Indian, a combined calendar which was an extension of his intent to start a combined religion named the Din-e-Ilahi.
This new calendar, called the Tarikh-e-Ilahi or the calendar of God, was started in 1584 AD, the Scroll article said.
Akbar's interest in a new calendar was because of practical purposes
According to many historians, Emperor Akbar showed interest in the new calendar because of practical reasons. As per the Historical Dictionary of the Bengalis, the Mughals were facing problem in collecting land revenue. They had followed the Islamic Hijri calendar and since it is lunar and did not coincide with the seasons, there was bound to be confusion, said the article.
The emperor then decided to go for a new calendar which merged the Islamic calendar, the historical Bengali calendar based on Surya Sidhant, a Sanskrit astronomy text, and the emperor's own date of coronation, the Scroll article said.
The new calendar was a bit difficult to begin with. From the first year which was the date of the Hijra (Prophet Mohammed's emigration from the Mecca to Medina) to 1556 AD when Akbar's coronation took place, the calendar went on as a lunar one.
Till the year 963 (the year of Akbar's coronation as per the Islamic calendar), both Akbar's new calendar and the Islamic calendar went together and things changed only after that.
From the coronation onwards, the years ticked off as per the old Bengali calendar, which was a solar one and it settled the problem of coinciding with the seasons and helped the administration's efforts of levying taxes.
Formula to calculate Bengali new year today:
The formula for calculating the Bengali new year hence became: 963 (Islamic year of Akbar's coronation) + 2015 (current English year) - 1556 (the English year of Akbar's coronation). Currently, the answer is 1422, which is the Bengali new year that starts today, the Scroll article said.
Akbar's new calendar did not survive much beyond his lifetime but it remained in practice in Bengal and it became integral to both crop seasons and religion.