Wonga has written off a total of £220 million worth of debt belonging to 330,000 customers after admitting making loans to people who could not afford to repay them.
The payday lender will also incur around £35 million worth of costs as it will not impose fees and charges related to a further 45,000 customers.
The move, which comes after the regulator found Wonga had granted loans to some people after carrying out inadequate affordability checks, means that about 330,000 customers who are more than 30 days in arrears will have the balance of their loan written off and will owe Wonga nothing. A further 45,000 customers who are up to 29 days in arrears will be asked to repay their debt without interest and charges and will be given an option of paying off their debt over an extended period of four months.
While the firm has not given an average amount for the level of debt held by those customers who will see their loans completely vanish, £220 million divided by 330,000 comes to £666. The firm also announced today that it has put stronger lending criteria in place, meaning it will be accepting "significantly fewer" loan applications and some existing customers may find they can no longer use its service to get a loan.
Those who will see their loans either written off or have interest and charges knocked off represent around one fifth of the 1.8 million customers who have ever taken out a loan with Wonga in its seven-year history.
As Britain's biggest payday lender, Wonga currently has around one million customers. It will contact people by October 10 to tell them if they are included in the redress programme. Customers should continue making payments unless Wonga tells them to stop.
The company also said it has improved the online information it provides on debt and money advice, both at the application stage and when someone is declined a loan.
The announcement was welcomed by consumer campaigners who said payday lenders must be kept "on a tight leash", and by Archbishop of Canterbury Justin Welby, who called for " a financial system that gives access to the poor and hope for the poorest in our lands".
Most of the £220 million in write-offs has been placed in Wonga's accounts already and it expects the £35 million cost to feature in its accounting for the next year.
Earlier this week, Wonga reported seeing its profits more than halve last year after it racked up £18.8 million in costs relating to a scandal over fake legal letters. The company expects to be "smaller and less profitable" in the near term as it works to clean up its reputation.
City regulator the Financial Conduct Authority (FCA) has put payday lenders firmly under the microscope since taking over regulation of the sector in April.
FCA director of supervision Clive Adamson said: "This should put the rest of the industry on notice - they need to lend affordably and responsibly. It is absolutely right that Wonga's new management team has acted quickly to put things right for their customers after these issues were raised by the FCA."
The regulator has already strengthened the rules under which lenders are allowed to operate and plans to impose a price cap in January on the fees and interest charged by payday firms, to protect borrowers from escalating debts.
Payday firms currently have only "interim permission" to operate under the FCA's toughened regime and they will need to pass assessments in the coming months to get full permission to carry on.
According to short-term lending trade body the Consumer Finance Association, which represents firms including the Money Shop and Quick Quid but not Wonga, 54% fewer loans are being granted and the number of loans being rolled over is down by 75% since the FCA imposed its tougher rules.
When it took over regulation of consumer credit, the FCA requested information from Wonga which suggested it was not taking sufficient steps to assess customers' ability to meet repayments.
Wonga's new chairman Andy Haste said the need for change at Wonga is "real and urgent".
He added: "We want to ensure we only lend to those who can reasonably afford the loan in question and during my review, it became clear to me that this has unfortunately not always been the case. I agreed with the concerns expressed by the FCA and as a consequence of our discussions we have committed to taking these actions."
Wonga, which unlike many payday lenders has its roots in the UK rather than the United States, has a default rate of around 7% on its loans. In June, Wonga was ordered to pay compensation of £2.6 million by the FCA after sending threatening legal letters from fake law firms to 45,000 customers.
The regulator said Wonga had been guilty of "unfair and misleading debt collection practices" by creating fake companies to pressure struggling customers into paying their bills.
Going ahead, Wonga plans to overhaul the image it presents, in a way that cuts the risk of it inadvertently attracting the very young or vulnerable.
Wonga's cuddly, elderly puppets disappeared from TV screens in July and the firm has no immediate plans to launch a new advertising drive.
Richard Lloyd, executive director of consumer group Which?, said: "Wonga's announcement is better late than never for struggling borrowers but it's clearly a result of the regulator taking a tougher approach. The FCA must keep payday lenders on a tight leash."
Joanna Elson, chief executive of charity the Money Advice Trust, said: "These moves are a welcome step in the right direction. "Nevertheless we know that there will remain a large number of borrowers with payday loans who are struggling to cope with their debts."
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