We estimate the dynamical lifetime of the Tesla to be a few tens of millions of years.
— Rein, Tamayo, Vokrouhlicky, The random walk of cars and their collision probabilities with planets, arXiv:1802.04718v1 [astro-ph.EP] 13 Feb 2018

In this paper, we have investigated the fate of the Tesla Roadster launched by SpaceX with their Falcon Heavy rocket on February 6th, 2018. The Tesla is currently on an Earth and Mars crossing orbit. Its first close encounter that may come within a lunar distance of the Earth will occur in 2091. On timescales significantly longer than a century, continued close encounters will render precise long- term predictions of the object’s chaotic orbit impossible.
However, using an ensemble of several hundred realizations we were able to statistically determine the probability of the Tesla colliding with the solar system planets on astronomical timescales.