By Paul Lewis
BBC Radio 4's Money Box
Hundreds of thousands of people in their 60s could get their state pensions boosted at little or no cost to themselves.
Strict contribution rules determine the level of state pension
The government is writing to nearly half a million retired people who get a reduced pension inviting them to pay extra National Insurance contributions.
The extra money they receive will be back-dated and may be enough to cover the cost of the missing contributions.
And their pensions will remain higher for the rest of their lives.
This situation had arisen after mistakes made by officials in 1996.
They stopped sending out letters telling people their National Insurance record was deficient. As a result, millions of people lost the chance to fill any gaps.
When this failure came to light in 2003, the government decided to write to everyone affected to tell them about the gaps in their record and how they could fill them.
It started with the 10 million people still in work. And now the government is writing to 483,000 people who have already retired.
Some people may have been paid too little pension for seven years.
To get their pension paid in full they will have to pay just over £300 for each year that is missing.
And each year filled could boost their pension by £2.50 a week, or more than £125 a year.
But Liberal Democrat MP Steve Webb told BBC Radio 4's Money Box programme it could be free money:
"If it is some years since they retired when they make this extra contribution, they will get extra pension not just for the future but back-dated to when they became a pensioner.
"If that is several years ago the extra pension they get back-dated could be more than the money they hand over.
"So it could be free money. They may not have to hand over any cash."
The government has agreed that any back-dated pension will not affect any means-tested benefits which have already been paid such as pension credit, council tax benefit or help with rent through housing benefit.
But the extra pension will affect entitlement in future.
Speaking on Money Box, Gary Vaux of Hertfordshire County Council's Money Advice Unit said not everyone would benefit from making further contributions:
"The situation is... complicated... For example, a lot of married women who already have a full pension based on their husband's contribution record, a lot of widows who are in the same situation... there is no point in them making up the contribution that will give them a pension no greater than what they have already got."
The National Audit Office revealed this month that the total cost of the exercise could be £100 million in administration and could boost pensions by £103 million.
BBC Radio 4's Money Box was broadcast on Saturday, 22 January, 2005, at 1204 GMT.
The programme was repeated on Sunday, 23 January, 2005, at 2102 GMT.