Final answer:
The correct answer is a lockbox system, which is used by banks to streamline the collection and deposit of company payments. It benefits companies by enhancing cash flow, reducing processing times, and improving security.
Step-by-step explanation:
The system in which customers send their checks to a post office box that belongs to a bank is called a lockbox system. In a lockbox system, a bank provides a service to companies by collecting payments mailed to a post office box and then depositing them directly into the company's bank account. This system improves cash flow management and reduces processing times for the companies that use it. Moreover, it enhances security by reducing the amount of time checks are in the mail and potentially subject to loss or theft.
A payment system is vital as it helps an economy exchange goods and services for money or other financial assets. In contrast, a depository institution is a financial institution that accepts money deposits and then uses those funds to make loans. Businesses and people rely on banks to store money in demand deposit accounts, or checking accounts, that allow for easy withdrawal or writing of checks, thus facilitating smooth financial transactions in the economy without the need to carry large amounts of cash.