ANZ cut its savings account rates yesterday - the last of the big banks to adjust deposit rates in response to the Reserve Bank's cash rate cut earlier this month.RateCity reports that the big banks' bonus (or conditional) saver rates and introductory rates have been cut by between 20 and 31 basis points.ANZ made the smallest cut of 20 bps, which was still more than the 18 bps of rate cut it passed on to home loan customers. CBA made the biggest deposit rate cuts.ANZ: ANZ cut its Progress Saver rate by 20 bps to 2.2 per cent (account holders must deposit a minimum of $10 a month and make no withdrawals). It cut the three-month intro rate on its Online Saver account by 20 bps to 2.1 per cent, and the base rate by 20 bps to 30 bps.Commonwealth Bank: CBA cut its GoalSaver rate by 30 bps to 1.7 per cent (account holders must deposit a minimum of $200 a month and make no withdrawals).It cut the five-month into rate on Netbank Saver by 31 bps to 2.2 per cent and the base rate by 20 bps to 30 bps.NAB: NAB cut its Reward Saver rate by 25 bps to 2.05 per cent (account holders must make one deposit a month and no withdrawals).It cut the four-month into rate on iSaver by 25 bps to 2.3 per cent and the base rate by 20 bps to 30 bps.Westpac: Westpac cut its Life account rate by 20 bps to 2.1 per cent (account holders must make one deposit a month and the balance must be higher at the end of the month).It cut the five-month intro rate on eSaver by 20 bps to 2.31 per cent and the base rate by 20 bps to 30 bps.Overall, 47 banks have cut savings rates since June 4, with an average reduction of 23 bps.The best bonus saver rates in the market are Ubank's 2.87 per cent, Bank of Queensland's 2.75 per cent, Endeavour Mutual's 2.75 per cent and ME Bank's 2.6 per cent.