Warren Buffett to the rescue -- again.

Berkshire Hathaway (BRK.A) has agreed to invest $5 billion in Bank of America (BAC), reviving the stock price and giving investors more faith in the financial sector's future. Shares of the bank rose 15% early Thursday, but by the close had settled to a 9% gain at $7.61.

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Buffett reportedly came up with the idea while sitting in the bathtub. So that's what billionaires think about while bathing. And it's a very sweet deal indeed: Berkshire gets 50,000 preferred shares at a 6% dividend, redeemable at a 5% premium. The company also gets warrants to buy 700 million bank shares at $7.14 a piece over the next decade.

If Berkshire exercises those warrants in full, it would own nearly 7% of the bank and become the biggest shareholder, The Wall Street Journal reports. Berkshire shares closed down more than 2% to $103,452.

Berkshire likely already earned more than $1 billion on the investment in the first day, Bloomberg reports. That's because, based on a $7.85 share price for the bank, the preferred shares Berkshire bought were worth $3.53 billion while the warrants were worth about $2.87 billion.

The share price dropped to $7.61 at the close, but the gain was still significant.

Bank of America was left in the awkward position of accepting the investment while insisting that it didn't really need the money. "I remain confident that we have the capital and liquidity we need to run our business," chief executive Brian Moynihan said, according to the Journal.

So why did he accept it? Because everyone thought that Bank of America was on its last legs, and no one's better than Warren Buffett at injecting some confidence into a company. "I also recognize that a large investment by Warren Buffett is a strong endorsement in our vision and our strategy," Moynihan added.

Buffett's been here before. In the financial crisis in 2008, he invested $5 billion in Goldman Sachs (GS) at a 10% dividend and a 10% premium. He also got warrants to buy $5 billion of common stock at a $115 strike price within five years. Goldman shares closed Thursday at just under $110.

Analysts felt better about Bank of America after the news. UBS took the stock off of its "least preferred" list, saying Berkshire's investment is likely to restore confidence in the shares. Wells Fargo analysts said there's a smaller chance now for Bank of America to raise money by offering common shares, which had worried shareholders.