Some accounts calculate interest on a daily basis, while others calculate interest on the minimum monthly balance or the average monthly balance. Some accounts pay a single rate of interest on the whole sum of money saved, while others pay marginal interest on savings made over a specified amount. Some banks pay no interest on balances below a certain level. It is probably best to operate a savings account that calculates interest on a daily basis, pays a single interest rate on the whole sum of money saved and pays interest right from the first dollar. However when considering these options, make sure the fees don't outweigh any gain.
Today there are a wide range of bank fees for administration and transaction costs on most accounts.
Banks can differ widely on how they structure these fees. If your NZ Superannuation is credited directly into your bank account, most banks will not charge you base or transaction fees on the particular account to which it is credited. Normal fees will still apply on any other accounts you operate. Crediting NZ Superannuation to your cheque or current account will save you money, as this will be your most active account and therefore the most expensive to operate. Check out the fees applicable on your accounts, and minimise withdrawals accordingly.