Not OP but I'll run what I plan on doing. In Germany you can get a plug-in ready kit with 2.2 kWh battery and 920W panels for less than 600€ [1]. The panels are about 1.8 m² each (=3.6 m² total), so with on average 1.200 kWh/m² solar radiation and 25% efficiency I'm looking at up to 1080 kWh in energy I'll get out of the system per year.
Electricity here in Germany is expensive at an average 30 ct/kWh, so the panels save 324€ worth of electricity - an ROI of > 50%. Choose some better quality for the inverter and battery and you'll still be north of 30% ROI.
The key thing making this high ROI possible is that it's small. Counterintuitive, yes - but explained by the fact that for larger installations than that, setup costs go up: you need to install the panels on your roof instead of hanging them off your balcony which can be thousands of € in labor, you need to run new power wires...
Your numbers are likely off by about half (in Germany your sunlight is less than 1200w/m2, panels are more like 22% effecient, you'll gave at least some cloudy days, your panels won't be tracking the sun.)
But a small system is still going to bring a return and is cheap to install. And it'll give you a real way to understand the concept and to experiment.
I started with a 660w small system, and it gave me lots of insight for planning my current system.
The inverter keeps a log of electricity generated, used, battery used, imported and so on.
I put that in a spreadsheet which calculates money saved. (Which is reasonably complex because of pricing tiers although fortunately I don't have to deal with daily pricing changes.)
Then some math returns the return on investment per month and per year.
Do you also subject the cost of upfront capital? Example: Imagine that you didn't have the upfront captial, and you needed to borrow it "from a bank" at X% for Y months.
Electricity here in Germany is expensive at an average 30 ct/kWh, so the panels save 324€ worth of electricity - an ROI of > 50%. Choose some better quality for the inverter and battery and you'll still be north of 30% ROI.
The key thing making this high ROI possible is that it's small. Counterintuitive, yes - but explained by the fact that for larger installations than that, setup costs go up: you need to install the panels on your roof instead of hanging them off your balcony which can be thousands of € in labor, you need to run new power wires...
[1] https://www.idealo.de/preisvergleich/OffersOfProduct/2092828...
[2] https://www.swm.de/unternehmen/magazin/energie/pv-ertrag-im-...