National Savings & Investments ( NS&I ) has just upped its rates on Premium Bonds and savings products – but they are still below the best paying ISAs and other savings accounts . From July, the Premium Bonds prize rate will be 3.8 per cent – after it had fallen from 3.6 per cent to 3.3 per cent in April . The odds on winning are also better, down from 23,000 to one to 22,000 to one for each bond held. So there should be an extra 322,000 prizes from the £60m pot. While the moves were welcomed by money experts, they note that NS&I was still far below rivals when it comes to savers earning on their cash. Sarah Coles, head of personal finance at AJ Bell, said: “It was starting to get a bit embarrassing for NS&I to have fallen quite so far behind the more competitive accounts in the easy access market.…