Several lenders announced cuts to their home loan rates last week, with the number of lenders offering rates below 3 per cent growing.ANZ cut home loan and deposit rates. On the home loan front, for borrowers with loan-to-valuation ratios of 80 per cent or less, ANZ cut the rate on its basic variable home loan (Simplicity Plus) by 12 basis points to 3.12 per cent.For borrowers with LVRs over 80 per cent, ANZ cut the rate on Simplicity Plus by 20 bps to 3.38 per cent.With these changes, ANZ is offering the lowest variable home loan rates among the big four banks. Simplicity Plus investor rates did not change.On the savings side, ANZ cut the base rate on its Online Saver account by 10 bps to 0.05 per cent. It also cut the three-month introductory rate by five bps to 1.55 per cent.The bank cut the majority of its term deposit rates by 10 bps. Its Goal Saver rate did not change.RateCity.com.au research director Sally Tindall says: "What's disappointing is that while the home loan cuts are largely reserved for new customers, the savings rate cuts will hit everyone with an ANZ online saver account."Westpac made big cuts to its investment property loan rates. The one-year rate on its Premier Advantage Investment loan (with principal and interest repayments) was cut by 50 bps to 3.19 per cent.The two and three -year rates were cut by 19 bps and the four and five-year rates were cut by 50 bps.  The best rate on offer is 3.09 per cent - for two and three-year terms.Westpac cut its interest-only investment loan rates by up to 40 bps.Bankwest cut fixed home loan rates by up to 125 bps. It is offering a three-year rate of 2.93 per cent for owner-occupiers paying principal and interest.For investors paying interest only Bankwest best offer is 3.49 per cent for three years.Bank Australia cut its basic home loan rate (for owner-occupiers paying principal and interest) by 30 bps to 2.95 per cent.