Did you know that if a company were to increase its dividends by 5% per year, it would take 14 years for its payouts to double? And if its rate of increase were 7%, then it would take about 10 years. That's why even if a stock offers a modest yield today, it can still be worth it for income investors to buy and hold.

A couple of stocks with the most aggressive dividend growth records you can invest in today are UnitedHealth Group (UNH -1.03%) and Broadcom (AVGO 2.02%). They have delivered strong results over the years, and shareholders have seen their income rapidly grow.

1. UnitedHealth Group

Health insurance giant UnitedHealth Group may not strike income investors as an ideal dividend stock to buy, as it yields just under 1.4%, which is below the S&P 500's current average yield of 1.7%. But over the past decade, the company has aggressively increased its quarterly payouts:

UNH Dividend Chart

UNH Dividend data by YCharts.

Its current quarterly payment of $1.65 per share is nearly eight times the $0.2125 per share that it paid shareholders 10 years ago. And it took just seven years for management to triple its payout from the $0.50 per share it distributed in 2015. That averages out to a compound annual growth rate (CAGR) of 18.6%.

That's an incredible rate of growth, and one that may continue given how strong its earnings are; the company's payout ratio remains low at 22%, which gives UnitedHealth plenty of room to continue making big increases to the dividend. And the business itself shows no signs of slowing down. CEO Andrew Witty expects that its bottom line will increase 13% to 16% annually over the long term, helped by continued expansion of its Medicare business.

Trading at 23 times earnings, UnitedHealth is modestly priced, though a bit more expensive than the S&P 500's average multiple of 20. But for this kind of growth and such an impressive dividend, the healthcare stock looks to be well worth the premium. 

2. Broadcom

If healthcare isn't exciting enough for you and you're craving a bit more growth potential, then semiconductor company Broadcom may be more of your style. With a yield of 3.1% at the current share price, the stock already has a much higher payout than UnitedHealth's. 

The company increased its quarterly dividend payment by 12% last year to $4.60. That's more than 10 times the $0.44 that it was paying as of the end of 2015, for a CAGR of 40% over that time frame. Given that its payout ratio is already around 62%, odds are that any future increases from Broadcom will be a bit more modest, but it definitely has room for more hikes.

Broadcom is coming off a strong fiscal 2022. For that year, which ended Oct. 30, net revenue rose by 21% to $33.2 billion. Profits increased by an even more impressive 74% to $11.2 billion. Those strong results led to the company announcing its 12th consecutive annual dividend increase. 

"As we look into fiscal 2023, our increased R&D investments during the preceding years position us to extend our leadership in next generation products within the end markets we address," said CEO Hock Tan.

What's been impressive over the past decade has been the company's solid revenue and dividend growth.

AVGO Dividend Chart

AVGO Dividend data by YCharts.

Trading at 22 times earnings, the tech stock is decently valued given the opportunities that exist in the global semiconductor market, which is expected to grow at a compound annual rate of 12.2% through 2029, when it will be worth around $1.4 trillion -- according to estimates from Fortune Business Insights. And when you throw in its high yield, Broadcom becomes an investment that could look great in any portfolio.