Permanent TSB is offering tracker customers 10% bonuses if they make addition payments of €5,000 up on their mortgages.
The offer is for residential, buy-to-let and commercial tracker mortgages but is only available until June 17.
It is also open to customers who are currently in arrears and the bonus payment will apply to any payments made once the arrears have been cleared.
'It's in both parties interest to reduce the amount of outstanding balances on tracker mortgages,' commented Permanent TSB's chief executive David Guinane.
But personal finance experts say the don't expect a large take up because people are either scared to spend savings or don't have savings at all.
"It's an exclusive offer for people with a lot of money," said Frank Conway, director at Moneycoach.ie
Some 60 per cent of PTSB's 180,000 mortgage customers have tracker mortgages and the bank has been desperate to persuade people to come off the dealas the cost the lender about €400m a year.
Experts have been warning customers in the last few weeks not to come off their trackers amid speculation that PTSB was going to offer cash incentives to those who switched to variable interest rates.
"A tracker mortgage holder is already paying about 30% discount compared a standard variable rate mortgage holder for the same loan," said Conway.
Today the bank said it would not be asking those who make the payment to give up their tracker in exchange for this payment.
However the deal will not be right for everyone.
Tracker mortgages customers will typically be younger customers as the deals were only available after 2004 and experts say if someone in their 20s, 30s or 40s have savings they would be better used to pay off credit card debt or saved for a rainy day, particularly with the continued threat of unemployment.
'Tracker mortgage holders are already on the pigs back and underpay for their borrowings by a significant margin' said Conway.
A comparison of payments on a €200,000 mortgage shows the tracker customer pay less than €764.49 a month, while the person on the variable pay more than €1,104.41.
This is based on a 30 year mortgage with the tracker customer paying 2.25% (1% above the present ECB rate) compared with a 5.25% variable rate.
Personal finance experts say the offer is probably best suited to older customers who are typically borrow less because they have already done their extensions and other work that would require either a new loan or use of savings.
"Age and life stage is an important factor - as we get older we are less likely to need to borrow again, so this offer will really suit those heading towards retirement.
"For a young family with future financial needs, they are probably better off saving for future needs and keeping the tracker for as long as possible," said Ciaran Phelan, chief executive of the Irish Brokers Association.
Conway says customers should also consider another issue if they do intend to pay down a lump sum - overpay and stick to your existing monthly payment or get the bank to reduce the monthly payment.
"If you are comfortable paying what you pay on a monthly basis you should stick to that. You are always better off paying more per month because you will pay the mortgage off earlier and save on total cost of borrrowing.
"It's a simple equation of time. The longer you take to pay the more expensive your borrowing is," says Conway.
He is of the view that customers in this present climate should always have a rainy day fund that could cover five or six months living costs in the event of redundancy.
He also believes few customers will take up the Permanent TSB offer given the recent Irish League of Credit Unions report which shows one in five people have just €70 left of disposable income each month.
"Cash continues to be king in the current environment and those with tracker mortgages are still paying next to nothing for mortgage financing…they need to think twice about the value of cash and the bargain they continue to enjoy through their tracker mortgage deals" said Conway.