In all likelihood, the dollar (Spanish dollar, remember) would still have been tariffed in shillings and pence in 1780, so there's no clash of units here. I find several references on-line to the different states having varying tariffs for the Spanish dollar in shillings - ranging from 6s to 7s6d and even 8s in New York. Others may correct me, but I thought "cents" only started in the later 1780s - shillings and pence would have been current before then, at least as units of account.

And in the UK, a "dollar" was slang for 5 shillings right through to decimalisation in 1971 (particularly in the expression "half a dollar", meaning a half-crown coin, which was a circulating piece, unlike the crown in later decades at least). The Brits also had the "Bank of England Dollar" in 1804 which, as far as I know, is the only UK coin to actually carry that word - it was overstruck on Spanish dollars so it made sense to retain the term.

A long while ago I wrote an article for Paper Money on the interest payments indicated on each state note of the 1780 series. I analyzed each state and quickly found out that the different states had different exchange rates of Spanish dollars into English money. This is well-known but the calculation by state was enlightening. The reference is: S.A. Feller, “A Rhode Island note, Spanish milled dollars, and English shillings,” Paper Money 111 (1984) 131.

I used the wonderful book by Eric Newman--The Early Paper Money of America that was published in 1976. Later on I upgraded to the fifth edition of this great book.

the pre-decimal British currency was known as the "£sd" system. So when I saw this, by the order I knew the "q" must be smaller than a penny. What I wonder is, 12 x 2½ = 30 farthings, which would be 0.7.2 (s.d.q). I have to wonder--where is the missing farthing? Is it a discount for paying a year in advance? More likely, it's just a rounding convention: squeezing an extra 1/48th of a penny (1/11,520 of a pound) out of a debtor each month, cannot qualify as a "get rich quick" scheme.

If, as indicated in Wikipedia, the Spanish-American peso of 8 reales ("Spanish milled dollar") was tariffed at exactly 6 shillings (£0.30) in Virginia, then the annual interest of 5% on two pesos would be 28.8 farthings (almost 7 pence and 1 farthing), while the monthly equivalent would be 2.4 farthings (almost 2½ farthings).

Maybe the promise of payment in those silver coins was because of the inflation/devaluation associated with the "continental currency"?

Pesos, with their halves (4 reales) and quarters (2 reales) were plentiful for larger values, while British copper coins, perhaps alongside local tokens, were still fairly plentiful for small values. However, Britain hadn't yet introduced the half farthing (this was in 1828, at first for use in Ceylon), although such a coin is mentioned in the Bible - Mark 12:42.

The U.S. dollar was first defined by the Coinage Act of 1792 and was introduced later that year - twelve years after this note was issued.

Further to the UK angle mentioned by Martin Purdy:

• In rhyming slang, an "oxford" (in full, "Oxford scholar") was a half-crown (two shillings and sixpence), or "half a dollar".

• The "Bank of England Dollar" (worth 5 shillings) dated 1804 was made by restriking Spanish-American 8 reales coins; some details of the original coin are often visible, proving that they were produced at least until 1811.

• Before that, the 8 reales (and 4 reales) coins were simply counterstamped with the head of George III - at first with an oval stamp as used in hallmarking, then with an octagonal countermark adaped from the punch for a Maundy (silver) penny; the 8 reales then passed for 4s 9d (4 shillings and ninepence), which gave rise to the expression of "two kings' heads not worth a crown". Also,

"The Bank, to make their Spanish dollar pass,
Stamp'd the head of a fool on the neck of an ass."

• Martin is right that this "1804" dollar was the only UK coin to carry the word "dollar" - indeed, it is the only coin of the British Isles to do so, though Scottish coins issued under Mary (1542-1567) and her son James VI (from 1567) included the Ryal or Dollar (originally 30 Scottish shillings, but later apparently 60 - either way, the equivalent of 5 shillings English) and the 1/3 and 2/3 thereof, but none of these coins bore any denomination; Maybe this is what led to the anachronism in Shakespeare's "Macbeth", in which (supposedly before 1040AD) Ross says, regarding "Sweno, the Norways' king" (presumably Sweyn Knutsson, 1030–1035):

"Nor would we deign him burial of his men
Till he disbursed at Saint Colme’s Inch
Ten thousand dollars to our general use."

With regards to the question on colonial money: Next mystery – Why denominate the note in dollars and then pay the interest in British money equivalents? We need to remember that the U.S. dollar was brand new, and the division into 100 cents had not even happened yet (in 1780) - Americans were used to dealing with British pounds, shillings and pence along with Spanish American reales, so it made sense to show equivalent values - plus, there were no U.S. coins to match.

If you look at the Continental Currency fractions (1/3, 2/3 etc of a dollar they make sense if you convert them into the British system - 18 pence (1s, 6d) and 36 pence (3s) respectively) they can be converted into change using British coins with the dollar valued at 4s 6d. Of course, it then gets complicated if you take into account the various state currencies and their conversions - New Jersey pounds vs pound sterling for example... anyway, it took a while to get everyone on the same system and then to provide coinage reflecting that system.