Which of the following factors influences a credit score?

Payment history is a critical factor influencing a credit score because it reflects the borrower's reliability in repaying debts. This component of a credit score accounts for a significant portion of the overall score, typically around 35%. Lenders use this information to determine the risk associated with lending money or extending credit; a strong payment history indicates that the individual has consistently made on-time payments, which builds credibility and establishes trust.

The other options are less relevant to credit score calculations. Monthly expenses, for instance, don't directly affect the credit score itself but can influence a person's ability to make timely payments. Similarly, investment returns pertain more to one's financial growth and are not part of the criteria for assessing creditworthiness. Lastly, the number of checking accounts a person holds does not directly impact their credit score, although it can be related to overall financial management. Thus, payment history stands out as the key factor in influencing credit scores.