How did Muhammad the Conqueror lead a large army to conquest almost every year of his reign without bankrupting the empire? How rich was the Ottoman Empire in the time of Muhammad the Conqueror?
That's it, though. Mohammed's constant campaigning has indeed put financial pressure on the country, and he has taken some controversial approaches to address the issue.
Siege of Belgrade in 1456. Muhammad's forces included tens of thousands of men and hundreds of cannons. That's not cheap.
First, there is a classic method of taxing farmers, namely Raya. Raya, a term sometimes used for Ottoman peasants, refers to the tax subjects of the Empire.
Secondly, he demeaned the currency, the silver akçe. Several times, actually. By the end of his reign in 1481, Akche had lost more than a quarter of its silver value. In this way, Muhammad truly became the successor of the ancient Roman emperors.
A coin from the reign of Mehmed II (r. 1444–1446, 1451–1481) minted in Ankara. Provided by Wikimedia Commons
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Third, and perhaps more controversially, Muhammad confiscated property belonging to the Waqfs and gave its proceeds to his soldiers.
Muhammad's successor, Bayezid II (grades 1481-1512), did not fight as frequently as Muhammad during his early reign (although he was not entirely at peace). Part of the reason was that his father had exhausted the treasury.
Imaginative portrait of Muhammad's successor, Bayezid. Partly due to the depletion of the treasury, Muhammad remained, and Bayezid would withdraw his troops from Otranto, a town in Naples recently occupied by Muhammad's army and would not have fought as many battles as Muhammad did. He also returned the charitable property that Muhammad had taken.
As for your second question, I do not know the specific amount in the Ottoman treasury in 1481, and even if I did, I do not know how to convert it into today's money. Rather, I would just say that his rule did not run fiscal deficits, which were not common until the late 16th century.
An Ottoman coin from 1576, during the reign of Murad III (reigned 1574-1595). By this time, the Ottoman treasury did run a deficit. In Muhammad's day, we have not yet reached that time.