Just a year after turning 18 and gaining access to a ton of trust money, Frances Bean Cobain is investing in the Los Angeles real estate market -- shelling out $1.875 million for a house all her own.

The 3,350 square foot Spanish-style home has 4 bedrooms, 3.5 baths, a terrace, vintage light fixtures and hardware, stained glass windows and a media room.

The 19-year-old rock heiress is reportedly attending college in upstate New York -- so this is just her West Coast crash pad ... in between semesters.