A loan is a sum of money borrowed from a lender that must be repaid over time, typically with interest. The borrower agrees to specific terms covering the repayment schedule, interest rate, and any associated fees. The original amount borrowed, before interest is applied, is called the principal, and each payment the borrower makes usually reduces this principal balance while also covering the interest that has accrued. The formal promise to repay is captured in a promissory note, which is the borrower's personal obligation to pay; when the loan finances real estate, a separate mortgage or deed of trust is recorded against the property as the security instrument that gives the lender a lien if the note is not repaid.
Interest is the cost of borrowing, expressed as a percentage of the principal, and it represents the fee a lender charges for providing the loan. With simple interest, the charge is calculated only on the original principal throughout the life of the loan using the formula \(I = P \times r \times t\), where \(P\) is principal, \(r\) is the rate, and \(t\) is time in years. Compound interest is calculated on both the initial principal and the accumulated interest from previous periods, so unpaid interest is added back to the balance and begins earning interest itself. This reinvestment causes the debt to grow exponentially and dramatically increases the total cost of borrowing compared to simple interest, especially over long horizons.
The distinction between interest and principal matters because most loans are repaid through a process called amortization, in which scheduled payments cover both components until the balance reaches zero. Early payments consist mostly of interest because the outstanding balance is at its highest; as the balance shrinks, a larger share of each subsequent payment reduces principal. Beyond personal finance, the term "amortization" also appears in accounting, where it describes the systematic expensing of an intangible asset's cost over its useful life, but the core mathematical concept of spreading a value over time is the same.