About this payment in particular, we know only that it was sent, apparently via the military road from the Roman fortress-city of Dara to the Persian fortress-city of Nisibis (Procopius, History of the Wars 1.22). We can, however, speculate productively.

The gold was likely sent in the form of coins. The gold coin of the late Roman Empire was the solidus (literally "solid bit [o' gold]"), called the nomisma in Greek. Since the solidus was struck at a weight of 72 to a pound, it would have taken a whopping 792,000 solidi to pay the Persians. Justinian and company, fortunately, had quite a few solidi laying around. Since the third-century demise of the silver denarius, gold had been the basis of the Roman currency; and solidi were minted in large numbers to pay the troops - and to be returned to the state via taxation. There were, in short, solidi aplenty in circulation. And in 533, before the expensive campaigns in North Africa and Italy and the ruinous impact of the plague, there were still solidi aplenty in the treasury. Justinian's predecessor had left him a surplus of 23,000,000 solidi; and though the Persian War and his earlier spending had dented that, there was almost certainly enough left in the imperial coffers to pay the Persians in gold coin.

Would the Persians have preferred a bullion payment? Possibly; their own coinage was primarily silver, and the fact that they requested the gold by weight may suggest that they expected to receive it in bulk. We know that some other payments to foreign peoples were made in solidi - later in the sixth century, the Avars would be paid anywhere from 100,000 to 800,000 annually - and this may suggest that coins were standard. A treaty later in Justinian's reign specifically mentions paying the Persians in gold coins. So let's go with the assumption that the Persians were paid in solidi.

How, then, were those 800,000 - odd coins conveyed? And from where? We don’t know, of course. It is possible that the coins were sent from Antioch, about 300 miles from Amida; it is equally possible that they came from Constantinople, 900 miles away by land. If we assume that they came from Constantinople, they may have traveled by sea to Antioch, and then overland from there. This, however, would not have been as much of a time-saver as you might expect, since the prevailing winds were not favorable. And of course, there was the risk of shipwreck. So let’s assume that the money traveled overland.

To transport the coins, the Byzantines would have used the heavy wagons of the imperial transport service (cursus publicus), which could carry up to 1,000 pounds each (the upper limit stipulated by law). We might imagine eleven or twelve wagons, each containing a few chests of coins and surrounded by an escort of mounted imperial guardsmen. Since the heavy wagons of the transport service only managed about 25 miles a day, it would have taken about 12 days to send the money from Antioch, and nearly 40 to dispatch it from Constantinople. Once the gold finally reached Amida, another day, under even heavier escort, would have brought it to Nisibis, and the Persians.

800,000 solidi to pay off the debt

What was the buying power of a single Solidi?

Or maybe more relevant, how many solidi were paid to a soldier for 1 years worth of service? ( and solidi were minted in large numbers to pay the troops ) and how many troops were in service? Basically what percentage of his yearly military budget did this equate to?

Pay in the Roman and Byzantine armies is really hard to calculate, not just due to limited evidence but also because it could come in various forms eg uniform and equipment, rations, and one-off bonuses, especially on accession of a new emperor. W. Treadgold (Byzantium and Its Army 284-1081 Stanford 1995) devotes a whole chapter to trying to work it out. It's part of his thesis that Roman military effectiveness corresponds closely to pay levels. He attributes a lot of the 3rd century instability to the fact that the basic pay was so poor the soldiers needed an accession bonus every few years to get by!

He cites M Hendy as giving 5 nomismata per year as basic pay but his own calculation is that Justinian inherited a pay scale of 5 nomismata for the lowest ranked infantry and 9 for cavalry but this was inadequate. In 545 he simply stopped paying frontier troops at all Treadgold assumes they must already have been moonlighting and Justinian let them carry on, while also allowing them to cultivate state land, and also issuing them with kit including clothes and fodder for horses. But he thinks the field armies were quite well paid and calculates the rate as 20 nomismata for infantry and 24 for cavalry