What is an agreement where a borrower promises to repay a lender at a future date?

The correct answer to the question is a loan. A loan is a financial agreement in which a borrower receives a specific amount of money from a lender, with the promise to repay that amount plus any agreed-upon interest by a specified future date. This relationship establishes the terms of repayment, including the schedule and any collateral that may secure the debt.

In contrast, a mortgage is specifically a type of loan secured by real estate, where the property itself serves as collateral for the borrowed amount. Credit typically refers to the ability to borrow money or access goods or services with the promise of future payment, but it is not an explicit agreement between borrower and lender regarding the repayment of a specific amount at a future date. Lastly, a lease is a contractual agreement for the use of property or equipment, which does not involve borrowing money in the traditional sense. Thus, the most accurate term for the borrower-lender agreement described in the question is a loan.