Roman Interest Rates

[Sauron]

During its decline, interest rates exploded in the complex Roman economy.  They had centuries of borrowing and lending systems.

Therefore they had to divide and multiply numbers easily and daily.

How did they calculate VI % of MMCXXI, I have never seen a system for using Roman numerals to divide or multiply ???

[Clanad]

It is quite a complicated task to add two Roman numerals together or even to subtract one from another, and multiplication and division are both extremely difficult. Mental arithmetic using the Roman numeric system would be beyond the capabilities of most mortal men. The dreary toil of the Roman accountant is reflected in the Latin name for the occupation, Tabularius 'the worker of tables'. The tabularius was a highly skilled - and thus highly valued - member of any senators household, though usually of the slave class, the lowest order of Roman society, he would be well looked-after for his services. The Roman accountant's task would be simplified to some extent by the use of an abacus, or by utilising a complicated system of counting using both the digits and finger joints of each hand.

Complicating matters further was the fact that the ancients had no concept of zero.  However, fractions were employed, albeit differently than what we utilize...The Romans didn't have a standard way to write fractions using their numerals. Instead, they just wrote out the word for the fraction: for example, two-sevenths was "duae septimae" and three-eighths was "tres octavae." The Romans did not have a word for every imaginable fraction: how often do you need to say thirty-three seventieths? If necessary, they would probably have said something like, "thirty-three seventieth parts," or "triginta tres septuagensimae partes."

Interestingly, up until the eighteenth century Roman numerals were used in Europe for book-keeping even though the arabic numerals we use today were known and in use from around 1000 AD. There are said to be two reasons for this:

Adding and subtracting are very easy with Roman numerals.

Arabic numerals can more easily be mistaken or forged - a 0 can look very like a 6 or an 8 or a 9 or be turned into one by a single stroke...

[Peter Pedant]

They used look up tables and then added

[Octavius]

The Romans did most of their practical calculations with fractions by using the uncia. The uncia started out as 1/12 of the as, a unit of weight (the word uncia is related to our word "ounce"), but it soon came to mean 1/12 of anything. You can add up twelfths to make halves, thirds, or quarters, so the uncia was fairly versatile.

When they wanted smaller fractions, the Romans usually cut the uncia into smaller parts. The system is very similar to measuring length in inches and fractions of the inch: you might not measure an object's length exactly, but you can still come very close.

You can find more about Roman numerals and mathematics here:  http://mathforum.org/dr.math/faq/faq.roman.html