One of the big changes to the AI in NA 2.2 is lending money. Lending money has been exploited by players to gain cheap, reliable casus belli, to build cheap or free manufactories, and as a powerful and reliable source of income for players who understood how the system worked. It appears that Paradox has been working to try and make loans fairer and more realistic, but it's not always transparent how things work now. I ran a series of tests to see how things worked, and I thought I would share my findings. Please keep in mind that I may be wrong about some of this - all I can share is what I have observed in my own games. If you find an exception or have a better rule, please post it here!
You should have no problem lending money to the AI in NA 2.2 as long as you follow four simple rules:
1) Keep interest under 9% and preferably at 4%. (Some countries will not accept loans in the 5-8% range, others will)
2) Only offer 12-month or longer loans.
3) Only lend money to countries with whom you have at least -50 relations.
4) Keep the amount proportional to the AI's economy.
Keep in mind that having the AI accept a loan isn't the same as a guarantee it will pay you back! Borrowers are very likely to default on a loan if its relations with you drop too low or if it has a casus belli against you (such as a core).
the Duration of the Loan
The AI never accepts loans that are shorter than 12 months. As soon as the loan drops to 11 months or less, chances go from "Very Likely" to "Impossible." This was mentioned in the patch notes and was probably done to make it harder for players to give a one-month loan purely to get a casus belli.
Duration does not seem to matter as long as it is over 11 months. I have never seen the AI be willing to accept larger amounts or greater interest rates with longer loans.
the Interest Rate of the Loan
The AI never accepts loans that have an interest rate above 8%. As soon as interest rates hit 9% or more, chances drop from "Very Likely" to "Impossible."
The AI will never accept a loan if the duration in months multiplied by the interest rate is 100+.
The AI considers interest under 4% to be equivalent to 4%. Dropping a loan below 4% (or sometimes 5% - it's hard to say) doesn't make the AI more likely to accept it or willing to accept a larger loan. This is hinted at in the patch notes, which mention that the AI is now much less likely to accept 1% loans, as players were using this as an exploit to get the AI to accept a loan when they ordinarily wouldn't have.
Amount of the Loan
The minimum loan a country will accept is equal to four months income.
Richer countries accept larger loans than smaller countries. As Burgundy or France I could lend around 1,000 ducats to a small, independent country like Lorraine (3 provinces) or Alsace (1 province), but both France (17 provinces) and Burgundy (13 provinces) were willing to accept much larger loans of more than 5,000 ducats (all my money), and Austria (9 provinces) was willing to accept at most a loan of 4,700 ducats, while Aragon (10 provinces but poorer than Austria) would accept only 3,000. From these findings, it appears that the AI uses plateaus or tiers (e.g. "all countries of under 4 provinces will accept 1,000-ducat 4% 12-month loans") rather than a set formula (e.g. "countries will accept 4% 12-month loans equal to 25% of their annual income").
The AI will accept larger loans if the interest rate is lower, but only so much. In one test, a one-province minor was willing to accept a 12-month loan of: 617 ducats @ 8% interest or 720 ducats @ 7% interest or 823 ducats @ 6% interest or 1029 ducats @ 5% or lower interest. This part of lending money is still confusing; sometimes the AI will accept loans between 5-8%, and sometimes it never accepts a penny if interest is above 4%. I'm not sure why.
Relationship between Lender and Borrower
The AI never accepts loans if its relations with you are lower than -50. I have had success lending thousands of ducats money to countries with -15 and -20 relations, but the same countries at -55 and -65 refused any loan whatsoever. The cutoff is somewhere between -20 and -55, and -50 seems a likely candidate.
Relations do not matter as long as they are above -50. Lending money to the same country with -15 relations and +200 relations gave me the same results each time.
Religion does not matter as long as relations are above -50. I was able to lend money to the Ottoman Empire easily as Burgundy (different religion group) once I got my relations with them above -50.
Cores and Casus Belli seem to be irrelevant. When I insulted Austria, dropping relations to (slightly) negative numbers and giving them a casus belli against me, they were still willing to accept a 12-month loan of 4,649 ducats @ 4% interest. I was also able to get Burgundy to accept loans despite having cores on many of their lands! Keep in mind that having the AI accept a loan isn't the same as a guarantee it will pay you back; you should still watch out for cores and casus belli or you may end up having the borrower default on your loan.
The AI is certain about its decisions. I always had either a "Very Likely" chance or an "Impossible" chance. Basically, either the AI will accept your loan or they won't - there is no second-guessing or multiple diplomats needed now to get the AI to agree. Either they will right away or they never will.
Using Loan Exploits in NA 2.2
Using loans to get cheap Casus Belli: Now that loans are a minimum of a year in duration this technique loses a lot of its lustre. Players want the ability to declare war on their own terms, not what's going on in a year. In addition, this won't work with bitter enemies...if relations have soured below -50 (all too easy during war, or if you have a bad reputation) then you simply can't lend them money at all. However, it should still be a useful technique in some cases when you are on good terms with a country and want a casus belli.
Using loans to make a fortune (the "Re-Lending" strategy and the power of compounding interest): Previously, players could borrow money from the bank at 7-13% interest, then turn around and lend the same money to the AI for 10-20% interest. With a maximum interest rate of 8% it's still possible to make money from lending it to the AI, but it's no longer profitable to borrow money from your own people simply in order to lend it out to other countries. It might be possible to earn a small profit doing so if a country had lower interest rates (from a national idea, for example, or from certain religions in my mod), but it would be much less profitable than loans were in 2.1. In addition to the lower interest rates, the longer terms of loans mean that the player cannot use the profits of a loan to offer larger and more profitable loans every 5-6 months. This has a small but negative effect on profits for the most dedicated lenders by halving the rate at which you can compound interest.
Using loans to build cheap or free manufactories (the "Foie Gras" strategy): One trick in NA 2.1 was to release a vassal (of the same religion group), lend it thousands of ducats, and watch it build a manufactory - for the price of building its first manufactory rather than your fortieth. Even if the vassal never paid back your loan, you got a manufactory for thousands of ducats less than you would have paid yourself once you diplo-annexed it again. And if the vassal did pay back the loan, you got it for free - and made money from interest! It should still be possible to use this strategy under NA 2.2, although it is still a kind of exploit.