In general, it can be said that it easily pays off over the total financing period. Have some offers made for you; the kWp should be around €1100-1200 net for a system size of about 9-10 kWp. Slightly more if it is smaller and slightly less if you plan the system larger.
nms_hs, on the one hand, you save on your own consumption and on the other hand, you receive the feed-in tariff. Assuming:
Annual yield of the system: 10,000 kWh:
Total annual electricity consumption (air-to-water heat pump, controlled residential ventilation, household electricity): 7,500 kWh
Own consumption 30% of 7,500 kWh = 2250 kWh * current electricity cost 25.04 cents = €563 savings per year
Feed-in tariff 7750 kWh * 0.9875 cents = €765 remuneration
Yield €563 + €765 = €1,328 per year
System costs €12,500
That means the system pays off with interest and insurance in about 11-12 years. The higher the electricity price rises, the more savings the system brings you, and the payback period is shortened accordingly.