Last Wednesday, I predicted National Savings & Investments (NS&I) would boost its Premium Bonds prize rate. A day later, it did.

The new rate – rising from 3.3 pc to 3.8 pc – applies to the July draw when NS&I expects to dish out around 322,000 more prizes than this month.

The increase puts the Premium Bond rate above the Bank of England’s base rate for the first time in nearly four years. Your chances of winning will increase, from 23,000 to 22,000 to one for every £1 bond held.

Premium Bond fans love the thrill of the monthly draw – and the tax-free perk that comes with a win. NS&I is tempting us with higher prizes. There will be 12 extra £100,000 prizes from July, 24 more at £50,000 and 49 at £25,000. The number of £50 and £100 prizes will shoot up by more than 400,000 apiece.

The chance to become a millionaire gives NS&I a big advantage over competitors.

Banks and building societies can’t sell Premium Bonds – but a few offer monthly prize draws linked to savings accounts. Prizes are smaller but you earn guaranteed interest.

Among the latest is Santander with its First Home Saver easy-access account.

One saver a month between now and December will win the £10,000 prize, a boost towards your first home deposit. To enter, you add at least £100 to your account each month. Each £100 increase gives you one entry to the draw.

You earn 4 pc on your money if you don’t make more than two withdrawals in a month.

Every month Kent Reliance dishes out £1,000 to one lucky saver with at least £100 in their account. You are automatically entered for the draw.

As it pays competitive rates (4.05 pc on the Limited Access Saver account, for example), it is an attractive addition to your account.

Family BS Windfall Bond demands a high £10,000 to qualify for its prize draw and pays an interest rate of just 2.75 pc. 

But it dishes out bigger prizes – ranging from £100 to £50,000 each month. You can withdraw your money at no charge if you give the society 35 days’ notice.

App-only Chip has a monthly draw with one prize of £10,000. But given the Prize Savings Account offers no interest, I’d avoid it.

Meanwhile, Revolut launched a prize draw last week. Customers set a weekly savings goal between £10 and £50, and those who maintain their ‘savings streak’ in a month qualify for a £10,000 draw.

Those who continue their streak for at least 50 out of 52 weeks are entered for a chance to win a £100,000 jackpot. The account pays 3 pc interest.