If I have both the Linguist virtue (*1.25 to advancement totals and xp spent in character creation to learn languages) and say, Afffinity With Latin (*1.5 to advancement totals and xp spent in character creation to learn Latin), how much xp does it take to get to Latin 5?
Would it be 40 xp?
(75/1.875)
I'd say x1.5, then multiply by 1.25 for a total of 1.875.
There's nothing I know in the book that says multiplication is additive, and there's at least 1 canonical case where they multiply.
Multiple rolls of 1 don't go X2, X3, X4, they go X2, X4, X8.
I agree with multiplying then multiplying.
That does still leave the question of rounding. You round up with Affinity and with Linguist. Let's say you have a Source Quality of 10. 10 x 1.5 = 15; 15 x 1.25, rounded up = 19. But 10 x 1.25, rounded up = 13; 13 x 1.5, rounded up = 20. So we're getting different results based on the order in which we apply them. Ugh. Now, you could round off in the end. 10 x 1.5 x 1.25, rounded up = 19. But this will always give you the worst result, maybe even worse than either order can give. To see this, let's look at a Source Quality of 1. 1 x 1.5, rounded up = 2; 2 x 1.25, rounded up = 3. And 1 x 1.25, rounded up = 2; 2 x 1.5 = 3. (Yay, agreement.) But 1 x 1.5 x 1.25, rounded up = 2. So rounding off at the end sometimes introduces a penalty. As you generally don't need high language scores, I'd tend to rule in favor of helping Affinity rather than hurting it. Of course, there are exceptions like with Pictish.
The advantage in such a high latin score is writing books really quick, so some people might consider it abusable?
Generally the rules text seems to favour giving you the better number, but I would think rounding is done at the end, since that's what you'd do in a more complicated operation? It's generally gonna give me like at least 8 extra xp after character creation (Apt Student and Book Learner as well, so I'll be getting my Latin learning in decent chunks)
How abusable is it that way really? You spend a point of Virtues on Affinity with Latin, gaining approximately +2 to your score. So now your Latin 7 (appropriate specialty) becomes 9ish. Communication hasn't changed. Let's look at the best-case, likely scenario: Com +3. So you get it done in 11/13 of the time. That's not a big savings. Let's say you write 2 seasons a year. After 5.5 years you've saved 2 seasons. Or you could take Personal Vis Source and have effectively saved in the ballpark of 5.5 seasons distilling vis.
Which complicated operations? Certainly not in US taxes. Also, here, that would mean you're not following the text of either Virtue, but rather doing half of one, half of the other, and then the second halves of the two together. Usually you apply one Virtue and then apply the other, right?
For what it's worth, Puissant is generally better than Affinity if your target score is 8 or less, unless you want to serve as a teacher, or you toss in 1xp at a time to benefit from the rounding bonus (in the latter case, it's still better if your target score is 6 or less).
Educated, in addition to giving one access to Latin in the first place if you haven't it from other sources, also beats Affinity with a target score of 7 or less, with no limitations on teaching (and it beats with a target score of 5 or less even with the full rounding bonus, being within 2xp with a target score of 6 or less). If you are specifically aiming for Latin, Baccalaureus is even better (90xp!).
That's all just as true or truer when there's other stuff contributing, such as Linguist.
Frankly, in most cases Affinity or Puissant Language is really not worth the effort, even for a grog. Linguist might, if you are really into building a polyglot from character creation, with several hundred xps devoted to languages.
If you want a magus with a ridiculous score in Latin, your best strategy is to create a grog with a ridiculous score in Latin and who's very good at Teaching, and have the grog instruct the magus over a few seasons.
In proper math. We're not talking about barbarians here 
I guess I meant like, general maths - you shouldn't round until the end because of things like this - it means you have to keep track of which order you did individual instances of the same operation (its BIDMAS, not BIDM(1)M(2)M(3)AS)
I don't know about US taxes, but from everything I've heard it seems like they're senselessly arcane, and I definitely don't envy people who have to deal with them lol
I'm looking to get a much higher score that 7 - I can get it to 15 during character creation before play (Magister In Arbitus, Educated, Privileged Upbringing) if I really want to.
I probably won't, but this is for a mythic companion centered around being a scholar or teacher, so it'll be decently high. But I could.
That's just not true at all. If f(x) is 1.5x, rounded up, and g(x) is 1.25x rounded up, then using proper math with f(g(x)) rounds up twice separately.
My old math professors would like to disagree.
I might take Puissant as well, but I'm focused on what I should do about the maths at the moment
Yeh, that's not true. Look at the example I just replied to Tellus with.
Where it is true is when you're not supposed to round but you need to round because you don't want to spend forever writing something out. That's why, when doing algebraic calculations, you're best off plugging things in at the very end, cutting down on compounding errors.
Yes, truly senselessly arcane, so needlessly "complicated operations," right?
You must be using a house rule. Still, if you devote that much to it, is it really abusive? What if I just dump that much into a bunch of other things?
I sincerely doubt that. This is how functions work. If they've reached that level of math, they know this, too.
Hey I'm not very good at maths but I did just plug this into a function calculator and it's not rounding between steps, I'm getting 1.875 instead of 2 or 3
I suppose there's a cap of 9 during character creation so that's technically as high as I can get it before play starts, but I'm still saving myself 100 xp that way, so it feels worth it
Then you didn't plug in Affinity and Linguist properly. Look at your own BIDMAS (we say "PEMDAS"). Rounding isn't multiplication. So why are you putting it in the order of multiplication? You're telling me you didn't follow BIDMAS properly and so go the wrong answer. Let's say it's Linguist then Affinity. This is what you get with 1:
(1 x 1.25 + 0.75) x 1.5 + 0.5
or the other order, Affinity then Linguist:
(1 x 1.5 + 0.5) x 1.25 + 0.5
That's what we get when we include rounding in BIDMAS. Are you telling me that you can just ignore those brackets/parentheses and additions with the ordering when you do BIDMAS?
Well, Affinity does raise that cap. Of course, you might not want to be old enough for that cap, either.
I wrote it out the way you did in your other post, 1.5(1.25(1)), as a single operation - it seems like you're seperating out the two? My reading of the interaction is that they both just multiply, I don't see why you'd round in between steps, maybe I'm misunderstanding
I note that Linguist doesn't tell you to round the result. It is perfectly reasonable to rule it should round up, just like Affinity, but it doesn't actually say that.
So, applying Linguist first, Affinity next, and only rounding at the end would satisfy RAW and only include a single rounding step.
Has it not hit the errata yet? That was an oversight I'd noted a while ago. It should hit the errata at some point if it's not already there.
It is not there - I checked.
There hasn't been any updates to the published errata for the last year.
But that's not what I wrote, is it? You deleted the rounding parts.
Because both Virtues (with the erratum) tell you to round, not just one of them. So to apply one Virtue and then the other, the proper mathematics is to round twice. Now, you certainly could pull the Virtues apart and apply pieces of them separately. Is there anywhere else we ever do that?