Aura currently pays $\$800$ each month to rent her apartment. Due to inflation, however, her rent is increasing by $\$50$ each year. Meanwhile, her monthly take-home pay is $\$1500$ and she predicts that her monthly pay will only increase by $\$15$ each year. Assuming that her rent and take-home pay will continue to grow linearly, will her rent ever equal her take-home pay? If so, when? And how much will rent be that year?