NatWest is offering £150 to anyone switching to it - and customers can now earn 3% interest on up to £150 a month as well.
The bank will pay £150 to anyone who opens an account using its mobile app before 5pm on April 7.
To get the cash they also have to deposit £1,250 into their new NatWest account and log in to its app before May 12.
In addition, NatWest has also sweetened the interest rate on its digital regular saver account.
This is only open to people who have a NatWest current account, and used to pay 3% interest - but only on up to £50 a month.
But now the deal pays 3% interest on up to £150 a month.
However, once NatWest savers have built up £1,000 in the account the interest rate drops to 0.25% on balances up to £5,000, and to 0.1% on anything above that.
The whopping 3% rate is far better than savers can get on any other regular saver account - the type of savings deal that rewards people for putting cash away at intervals.
Most regular savers are launched by small building societies, rather than big firms like NatWest.
Many are designed to help customers develop a savings habit and pay for one-off yearly events - like Christmas shopping.
The best rate on the open market is 2%, from Saffron Building Society, and savers can only put in up to £50 a month.
The second-best rate is 1.2%, from Furness Building Society, though its customers can put in as much as £250 a month.
The 3% NatWest savings rate, while welcome, is still outstripped by inflation - which is currently above 5%, and could reach 8% in months.
Inflation is a figure which shows the rough increase in the cost of goods and services.
If inflation is higher than the interest paid on a savings deal, any cash held in that account is losing money in real terms.
That is because what you can do with that cash in the real world falls faster than the interest it earns.
However, savers should not lose heart, as any spare cash has to be held somewhere and it makes sense to look for the best deals possible.
Deals from companies overseen by the Financial Services Compensation Scheme (FSCS) are safe havens for any spare cash - though this might be in short supply due to the cost of living crisis.
This is because the FSCS guarantees that even if the savings provider goes bust, up to £85,000 of an individual's money is protected.
The cost-of-living surge coming in April is “the worst” crisis Brits have faced in 22 years including Covid and the financial crash, Martin Lewis declared yesterday.
TV’s Money Saving Expert issued a desperate direct plea to Chancellor Rishi Sunak ahead of Wednesday’s Spring Statement to offer more help to the poorest Brits.
