DES MOINES, Iowa — Americans who were afraid to open their 401(k) statements during the recession are finding good news inside the envelope now: For the most part, their accounts have come all the way back and then some.

Nine in 10 of the popular retirement plans are at least back to where they were in October 2007, the peak of the stock market. Since the bull market began in March 2009, stocks have almost doubled.

And many investors who kept their nerve and continued putting some of their paycheck into a 401(k) during the market’s worst months are now ahead.

“I thought it would be more like six to eight years of pain, so I’m more than happy,” says Brett Hacker, a photographer for a TV station in Kansas City, Mo.

The married father of two says most of his account is invested in a mutual fund that tracks the Standard & Poor’s 500 index, and the rest in Meredith Corp., his employer. His balance fell 53 percent in the downturn. He’s now 15 percent ahead of where he stood in 2007.

“By the time that the market started going down, I thought it was too far gone to jump out — and I just let it ride,” Hacker says. “I figured that I was in for a long haul.”

Account balances didn’t recover entirely from the strength of the market. Those automatic paycheck deductions helped a lot.

On average, 401(k) participants put in about 8 percent of their pay from 2003 to 2006, says business consulting firm Aon Hewitt. Contributions slipped slightly during the recession, falling from an average 7.7 percent in 2007, to the current average around 7.3 percent.

Advisers typically recommend setting aside from 11 percent to 15 percent of your salary to enable you to live comfortably in retirement, and ensure you save enough to last for decades.

A 401(k) plan allows employees to deposit part of their salary into an account and not pay income tax on the money until it’s later withdrawn in retirement. Employers may also match a certain portion of a worker’s contributions. Taking money from the account prior to age 59Z\x will trigger taxes and a penalty.

An analysis of balance data provided by the nonpartisan Employee Benefit Research Institute shows the youngest workers with the shortest time on the job saw the most significant recovery.

Those who bailed out of stocks near the bottom locked in their losses — and if they were afraid to reinvest, they lost out on the recovery.