You do, but even if it's paid for, you still have to pay taxes, insurance, and maintenance on it. It's likely better than renting in most cases, but it's not a free place to live.
It's still an income-producing asset. It produces quite a lot of income. You have to pay for maintenance on everything, but that doesn't mean that income-producing assets don't exist.
It's still an income-producing asset. It produces quite a lot of income. You have to pay for maintenance on everything, but that doesn't mean that income-producing assets don't exist.