The house can only be bought if you play through the story. If you grind money, you are wasting your time. Even if you cheat code your way to the money listed for the house, it is STORY LOCKED until it becomes available.
We've unfortunately had a few people who have done the grind for 500+ days of Training to make the money, completely avoiding the gameplay.
If you read the blue instruction guide presented on Day 12 immediately after your character finishes meeting Ramoray, you would have seen that the car and house become available later in the game.
