Pfizer (PFE -3.07%) stock has struggled over the past year, losing around 28% of its value. Its dividend payout, meanwhile, has continued to rise again and again. This combination has pushed the dividend yield up to nearly 6%.

Is this your chance to secure a generous income stream of dividends?

Earn $1,000 in dividend income with this strategy

With the current dividend yield at 5.9%, you would need to invest around $17,000 into Pfizer stock to earn $1,000 in annual income. If you wanted to earn $1,000 in monthly income, you'd need to invest roughly $200,000.

Don't have that much to invest? Don't worry. By starting with a smaller amount, you can gradually build up to earning $1,000 in passive income. There are two pathways to achieving this goal.

First, there's a chance that Pfizer stock has significant upside from here. The company's COVID-19 vaccine, Comirnaty, saw its sales fall faster than expected last quarter, dragging down overall results. Total sales, for instance, fell by 19% year over year. When excluding COVID-19 revenue, however, sales actually increased by 11%. This suggests that Pfizer's core business is still strong despite a slowdown in COVID-19 vaccine demand. With a strong pipeline of potential new products, it's possible that the market is overreacting to short-term headwinds.

Second, Pfizer stands a good chance of increasing its dividend further in the years to come. It already has 15 years of consecutive dividend raises under its belt. New product launches -- like its upcoming oncology treatment, Padcev, which could contribute billions of dollars in new revenue -- should help raise this payout further over the long term.

In combination, long-term share price appreciation and dividend raises could help a small initial investment grow into a sizable nest egg. It may take some patience, but it's very possible to generate a $1,000 passive income stream using Pfizer stock.