How is compound interest calculated for loans?

Compound interest on a loan is the process by which interest accrues on both the original principal and on prior interest that has been added to the balance. The standard mathematical expression used in education and personal finance is A = P (1 + r/n)^(n t) where A is the future amount owed, P is the initial principal, r is the nominal annual interest rate expressed as a decimal, n is the number of compounding periods per year, and t is the time in years. Sal Khan at Khan Academy provides accessible demonstrations of this formula and its use in typical consumer lending examples.

How the formula works
Each compounding period applies the interest rate for that period to the current outstanding balance. If interest compounds monthly, the annual rate is divided by 12 and applied twelve times per year. Over multiple periods, interest charged in earlier periods becomes part of the balance that later interest calculations use. This is the mechanical cause of exponential growth in the amount owed. For a one-year loan of one thousand dollars at twelve percent annual interest compounded monthly the calculation is A = 1000 (1 + 0.12/12)^(12) which yields the principal plus the compounded interest for that year.

Compounding frequency and APR versus effective rate
Different lenders express rates in different ways. The Annual Percentage Rate often reported to borrowers can obscure the effect of compounding frequency because it may not reflect the effective annual rate that results when interest compounds more than once per year. The Board of Governors of the Federal Reserve System issues consumer guidance explaining how disclosure of APR and compounding affects borrower understanding and the total cost of credit. Borrowers who do not compare effective annual rates may underestimate the long-term cost of a loan.

Relevance, causes, and consequences
Compound interest matters for individual financial decisions, household budgets, and broader inequality. The cause is the contractual choice of compounding frequency and rate; consequences include faster-growing debt burdens when interest compounds frequently or when rates are high. On the other hand, compound interest works the same way for savings, illustrating why early saving is powerful. Leora Klapper at the World Bank has documented how limited financial literacy and unequal access to transparent financial information can deepen disparities in credit outcomes across regions and demographic groups. In territories with weak consumer protection or informal lending markets, borrowers can face compounding arrangements or fees that quickly make small loans unaffordable.

Cultural and territorial nuances
Legal limits on interest rates, known as usury laws, vary widely and change how compound interest operates in practice. In some cultures informal lending practices replace regulated credit markets, producing different compounding behaviors and social consequences. Environmentally and territorially, the availability and cost of credit influence investments in housing, agriculture, and small enterprises; high compound interest can deter long-term investments that have social or ecological benefits.

Understanding the compound interest formula and watching for compounding frequency and disclosed APRs equips borrowers, policymakers, and community leaders to assess loan affordability and to design interventions that reduce predatory practices and improve financial inclusion.