I'm interested in the history of recurring payments. The farthest I could get to is the feudal system, where peasants paid rent to knights once every so often. Obviously the banking system in the late 20th century spearheaded a revolution in monthly subscriptions, but I am interested to find out whether there is a known record of any large-scale recurring mechanism system that been set in place during ancient times.
There are cases from Ancient Rome. For example, Rome's richest man, Crassus, sold houses on installment plans.
An article called Men at work: public construction, labor and society at middle republican Rome, 390-168 B.C has more examples. Here's one:
In the case of the Lex puteolana, the city of Puteoli was not liable for payment at once, but paid the total in two smaller installments at the leasing and then at the approval of the finished construction. This practice appears standard and helped to diminish the actual payments for which the state was liable.
Also, there's Carthage mentioned in another answer and Philip V who (starting in 196) had to pay 1,000 talents.
Half at once, half in installments over ten years (cancelled in 191: Polyb. 21.3)
Livy is also given as a source for this.
Here, from 428 BC, is a rather complicated real estate lease with a 60-year(!) term. 20 talents of dates per year, plus a number of other clauses and considerations.
Baga'miri, son of Mitradatu, spoke of his own free-will to Belshum-iddin, son of Murashu, saying: "I will lease my cultivated field and uncultivated land, and the cultivated field and uncultivated land of Rushundati, my father's deceased brother, which is situated on the bank of the canal of Sin, and the bank of the canal Shilikhti, and the dwelling houses in the town of Galiya, on the north, adjoining the field of Nabu-akhi-iddin, son of Ninib-iddin, and adjoining the field of Banani-erish, a citizen of Nippur; on the south, adjoining the field of Minu-Bel-dana, son of Balatu; on the east, the bank of the canal of Sin; on the west, the bank of the canal of Shilikhti, and adjoining the field of Rushundati, the overseer (?) of Artaremu---all to use and to plant for sixty years. The rent of the cultivated field will be twenty talents of dates; and the uncultivated field (I will lease) for planting." Afterward Bel-shum-iddin, son of Murashu, accepted his offer with reference to the cultivated field and the uncultivated field, his part and the part of Rushundati, his uncle, deceased; he shall hold for sixty years the cultivated portion of it for a rental of twenty talents of dates per year, and the uncultivated portion for planting. Each year in the month Tishri, Bel-shum-iddin unto Baga'miri will give twenty talents of dates for the use of that field. The whole rent of his field for sixty years Baga'miri, son of Mitradatu, has received from the hands of Bel-shum-iddin, son of Murashu. If, in the future, before sixty years are completed, Baga'miri shall take that field from Bel-shum-iddin, Baga'miri shall pay one talent of silver to Bel-shum-iddin for the work which he shall have done on it and the orchard which he shall have planted. In case any claim should arise against that field, Baga'miri shall settle it and pay instead of Bel-shum-iddin. From the month Nisan, of the thirty-seventh year of Artaxerxes, the king, that field, for use and for planting, shall be in the possession of Bel-shum-iddin, son of Murashu, for sixty years.
When the First Punic War ended in 241 BC there were a number of clauses in the peace treaty.
The next order of business was money. Rome wasn’t going to let Carthage walk away without handing over a large amount of talent. Carthage was to pay the Romans 3,200 talents over the next ten years. They also had to pay an indemnity of 1,000 talents immediately. Rome didn’t expect the Carthaginians to be able to pay the talents quickly. However, they paid it off much quicker than anticipated due to their new trade networks.
So one clause in the treaty required Carthage to pay Rome 3,200 talents over a span of 10 years. If paid in equal amounts at regular intervals that would come to 320 talents per year, or 26.666 talents per month, or 0.876 talents per day.
So depending on how those payments were made that could count as an example of regular periodic payments between governments in 241 BC. And it seems very likely that was not the first example in history.