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Some of the best-paying savings accounts seen in more than a decade have been released in the past week, but only if you qualify for them.

The new deals come after banks came under pressure from the Financial Conduct Authority (FCA) to raise their interest rates. “It is critically important that customers can benefit from competitive interest rates to protect the value of their savings," the FCA said last month.

The banks are now responding - the catch being that some of the top-paying rates have so far only been on offer to a bank's existing customers. 

Linked savings accounts are gaining attention as banks are offering top rates on the savings accounts that customers can open once they have a current account.

This provides extra incentive to either stick with your existing account or consider switching, to make the most of the competitive interest rates. 

So, we’ve rounded up some of the top interest rates on savings accounts available to existing customers of banks like Santander, Lloyds, Bank of Scotland and Virgin Money. 

Easy access 

If you have a Santander Edge current account, then it’s worth exploring the Edge saver, which has a mighty 7% interest rate. However, this is only valid on balances up to £4,000 so would work best for anyone that is keen to grow their savings pot throughout the year, or has a small pot set aside that could be earning more interest. The account can be opened with just £1 and withdrawals can be made at any time, so this is certainly a flexible way to save. 

Alternatively, Virgin Money’s Private Savings Account offers an interest rate of up to 5.61% for its customers. But, there is a catch, as you’ll need to have a big savings pot - £1 million to be precise - to unlock this. The interest rate drops to 5.09% for balances from £0 to £499,999. However, this rate is still competitive and is great for anyone that has a Private Current Account or Current Account Tracker. 

Regular saver 

If you would like to save little and often, a regular savings account can help.Since February, First Direct’s regular saver has been boasting one of the top interest rates in the market at 7%. This interest is fixed for 12 months and you can save between £25 and £300 a month, which works out at £3,600 in a year. Remember, you’ll need to be a 1st account holder to get access to this account. 

Elsewhere, Lloyds has a monthly saver with an interest rate of 6.25%. This works in a similar way to First Direct, as the interest rate is fixed and paid after 12 months. The good news is that you can save from £25 to £400 a month, and top up your savings by bank transfer as long as you don’t exceed £400. 

Cash ISA

Is tax-free savings something you want to explore? If yes, then Virgin Money has a one-year fixed cash ISA at 5.80% which is available for anyone that has a current account with Virgin Money. This is a very competitive interest rate as it beats the top interest rate that is open to everyone - as this is from Shawbrook Bank at 5.78%. 

Fixed-rate bonds 

Speaking of fixed-rate savings accounts, there are also some fixed-rate bonds which are only available to existing customers. Monzo offers a fixed-rate savings pot for customers with a current account at 5.60%. This is provided via Paragon and you’ll need £500 as a minimum deposit.

Bank of Scotland has a two-year fixed-rate bond which has a bonus 0.05% interest rate for anyone that holds a Bank of Scotland Personal Current Account that has been opened for at least 40 days. This means the interest rate is 5.55% for existing customers, but drops to 5.50% for new customers. 

These rates are competitive, but it’s always worth comparing savings accounts, as you may find a greater interest rate elsewhere. For example, Ford Money has a two-year fixed-rate savings account that is available to anyone at 6.05%, which comfortably beats Monzo and Bank of Scotland.