The offer is part of the building society’s £500,000 giveaway, which will give savers ten chances to win the top £20,000 prize.

It is also offering ten prizes of £10,000 and 40 prizes of £5,000.

To be in with a chance of winning, customers need to save £100 into a Nationwide ISA between 6 March and 30 April.

At the same time, Nationwide is increasing the rate on its triple access online ISA from 0.9% to 1.21%. As the name suggests, this account allows three withdrawals in each 12-month period. Subsequent withdrawals will lower the interest rate to 0.10% for the remainder of that period.

The new giveaway follows the launch of Nationwide’s Start to Save account and prize draw last month, which offers savers the chance to win £100 prizes for saving regularly.

Tom Riley, Nationwide’s director of savings, said: “At the start and end of a tax-year we see a spike in savers rushing to make the most of their tax-free ISA allowance. Our new prize draw rewards these savers by giving them the chance to win £20,000 – the equivalent of a full year’s ISA allowance.”

How the prize draw works

The draw is open to new and existing members and to qualify ISA balances need to be increased by £100 or more by the time the prize draw entry period closes at the end of April.

Existing members who meet the eligibility criteria will be automatically entered into the prize draw.

The draw is open to customers in England, Scotland and Wales and will take place on 21 May. Winners will be selected at random.

Prizes will be paid directly into an existing Nationwide account or by cheque.

Members can qualify either by opening a new account or by topping up an existing account. This can be done with new ISA subscriptions or by transferring existing ISA balances from other providers.

Andrew Hagger, personal finance expert at website Moneycomms, said: “ISA rates, like the wider savings market, are stuck in the doldrums and don’t look very attractive, so I can understand why Nationwide is making this move.

“The cash ISA market is stagnant and it’s a sad state of affairs that it’s got to the stage where some consumers need incentives to kick them into action.

“With 60 prizes up for grabs and a total prize fund of half a million pounds this move is likely to prove popular – particularly as you only need to deposit a maximum of £100 to qualify.”