Many countries in EU4 start with a tech level of 3, and at administrative tech level 4 you can build temples / churches. Somewhat unintuitively, these are economic buildings, as they raise the tax rate in the province you build them in. In a typical developed European province, building a church for 100 gold results in a raised income of 0.2 gold per month, or 2.4 gold per year, thus 2.4 yield, taking you a bit over 40 years to get your investment back. Which already means that over 400 years you get 10 times your investment back. And as long as you reinvest that into other buildings with similar financial yields, you can get that compound interest train rolling and be relatively rich later in the game.

But weirdly that isn't even the best or earliest method. Even before you unpause for the first time in 1444, you can already make a much more impactful financial decision, available to many countries: Razing all your fortresses. A fortress costs 200 gold to build, but costs 1 gold per month, 24 gold per year in maintenance. If you destroy your fort, within 8 years you earn the money to construct it back. And while higher level forts can have a big impact later in the game, the level 2 forts you have at the start of the game aren't terribly useful, especially on flat land. A mountain fort at your borders can have a bigger impact in a war, but if your warfare has economic problems, razing your forts and putting the money into your army probably has a better effect.

The game impact of compound interest in Europa Universalis 4 is lessened by gold being not the most important currency. Monarch power points in administration, diplomacy, and military are far more important, with an excess in the first two of those categories being easily transformed into gold income by spending them on province development. Most players with a decent gold income will transform that into monarch power points by hiring advisors. An advisor costs around his level squared in gold per month, that is a level 1 advisor around 1 gold, a level 2 advisor around 4 gold, and a level 3 advisor 9 gold. And that is only at the start of the game, the cost goes up by 0.5% per year, so in 1644 they all cost twice that. Hiring advisors will drain your gold, so most people won't constantly reinvest gold into buildings that get them more gold over time, and compound interest isn't such a big game design problem. If you played without advisors, it would also be likely that you'd run out of investment opportunities, as without spending monarch points on province development, you run into building limits quickly. On the other hand, developing provinces and increasing tax base and production results in a higher yield for your buildings.

Ultimately the effect of expansion in Europa Universalis 4 is a lot more powerful than economic gameplay. Playing "wide", that is to say conquering a maximum amount of provinces, is a lot easier than playing "tall", that is to say building up the value of existing provinces. That is not only true for the player, but also for the AI. In consequence, the map that starts out as quite a patchwork in 1444 tends to consolidate a lot in the centuries that follow. It will be interesting to see whether this remains the same in Europa Universalis 5, which starts over a century earlier. Because if it does, the EU5 map in 1444 would look a lot less patchworky than in EU4.