The Dow Jones Industrial Average and Bank of America both bounced back from disastrous Mondays to steady gains during Tuesday trading.

The Dow Jones finished the day up 429 points, or a 3.97 percent change, after plummeting more than 600 points on Monday.  

The Dow finished up in manic trading after the Federal Reserve announced it would not raise interest rates, but also wouldn't provide a quantitative easing or other relief.

"Since the 2008 crisis we've developed this thought that if we crash they'll spend $740 billion TARPs on you, they'll keep dropping rates on you. That's an unhealthy environment for investors," James Paulsen, chief market strategist at Wells Capital Management in Minneapolis, told CNBC. "To the extent that they're getting away from that and saying, 'stand on your own,' that's a very healthy event for today."

The gains don't mean that the economy is back on track, or that the Dow Jones won't see a major drop tomorrow, according to one analyst.

"It's normal to have a bounce back after the downward moves we've had," Pioneer Investment analyst John Carey told The Wall Street Journal. "The key is whether this is a sustained recovery or just a sign of bargain hunters coming in and picking up beaten-down stocks."

Bank of America Rebounds after Bad, Bad Monday

Charlotte-based banking company Bank of America Inc. (NYSE: BAC) had a bad case of the Mondays yesterday. The company got hit with a $10 billion lawsuit from American International Group (NYSE: AIG) and also saw a major hedge fund investor cash out his 17 million shares.

The company saw its stock plummet more than 20 percent, as some speculated that it may need to raise capital if it hopes to survive numerous pending lawsuits.

"They probably don't need to right now, but every day there's another lawsuit out there that has merit," FBR Capital Markets analyst Paul Miller told Bloomberg News. "How in the heck are they going to settle all these suits unless there's some way to break away from the Countrywide liabilities?"

On Tuesday, BofA saw its stock jump up close to 17 percent, as its CEO assured investors it was on the right path. The stock finished at $7.60, more a dollar above Monday's closing price.

BoA chief executive Brian Moynihan assured investors that the company can withstand the losses associated with its mortgage company, Countrywide Financials, and that it was going in the right direction.

"We are aggressively taking action to put the legacy mortgage issues behind the company -- even at great short-term cost -- and to help get the U.S. housing market going again," Moynihan wrote in a letter to employees. "We have weathered challenging times before and we will now."