A business offering cloud storage has a loyalty programme. When a user signs up, they receive $1\text{GB}$ storage for free, and every month after that they earn a further $100\text{MB}$ free until they have earned a maximum of $5\text{GB}$.

1. If a user signs up on $1^{\text{st}}$ January $2019$, how much free data storage will they earn by the end of their first year?

2. During which month and year will the user hit their limit of $5\text{GB}$?