New banks continue to offer savers the best fixed-rate deals as they compete with each other for your money.The top one-year deal comes from Charter Savings Bank at 2.07 per cent before tax (1.66 per cent after tax).French-owned RCI Bank, part of the Renault group, and FirstSave both pay 2.06 per cent (1.65 per cent), while Harrods Bank now offers 2.03 per cent (1.62 per cent) and Paragon Bank 2.01 per cent (1.6 per cent).In contrast the best deals from traditional banks and building societies are 1.75 per cent (1.4 per cent) from Leeds Building Society or 1.65 per cent (1.32 per cent) from Nationwide. Last week Halifax cut its one-year rate to just 1.15 per cent (0.92 per cent). EASY-ACCESS AND CASH ISASFor two years top deals include Paragon Bank at 2.4 per cent (1.92 per cent) along with RCI and Hampshire Trust banks at 2.35 per cent (1.88 per cent).The best rates on easy-access accounts include RCI Bank Freedom Account at 1.65 per cent before tax (1.32 per cent after tax).Post Office Online Saver pays 1.61 per cent (1.29 per cent) including a bonus for the first year you are in the account. After this the rate drops to 0.65 per cent (0.52 per cent).BM Savings' Online Extra Issue 19 pays 1.6 per cent (1.28 per cent), but once again the rate is boosted by a short-term bonus. It drops to 0.25 per cent (0.2 per cent) after 12 months.On tax-free accounts, Post Office Online Cash Isa pays 1.51 per cent including a 0.86 percentage point bonus for the first 12 months.Virgin Money Defined Access Isa is a slightly better rate at 1.56 per cent, but it limits you to making three withdrawals a year - although there is no bonus on this account.The best deal with no bonus and no withdrawal facilities comes from Nationwide's Instant Isa Saver Issue 3 at 1.4 per cent.On fixed rate cash Isas, Virgin Money pays a top 1.81 per cent for one year, followed by the new AA Savings deal (where the deposit taker is Bank of Ireland), at 1.75 per cent. Virgin Money pays 2.06 per cent for two years. Find the best cash Isa or savings account for you.