What typically influences the interest rates offered by banks on deposits?

The correct answer highlights that interest rates on deposits typically depend on a combination of market competition and federal regulations. Market competition plays a crucial role because banks need to attract customers by offering competitive interest rates. If one bank offers higher rates, others might follow suit to retain or attract more depositors.

Additionally, federal regulations also influence interest rates. Regulations set by entities like the Federal Reserve can impact how much banks need to pay for deposits. For instance, changes in monetary policy can lead to adjustments in baseline interest rates, which in turn affects the rates banks offer to their customers. This creates a dynamic environment where both competitive pressures and regulatory frameworks work together to shape the interest rates offered on deposits.

Other factors mentioned in the other options, such as the central bank's decisions alone or the income of depositors, may influence interest rates but do not encompass the broader economic environment or regulatory landscape that drives deposit rates. Similarly, focusing solely on the size of a bank's assets overlooks the competitive nature of the banking industry and external regulatory influences.