Compound Interest in Engineering Economics

Compound interest is a fundamental concept in engineering economics, describing how interest accumulates on both the initial principal and previously earned interest, causing exponential growth of investment value over time. The core formula for compound interest is $\displaystyle A = P(1 + \frac{r}{n})^{nt}$, where is the accumulated amount, the principal, the annual interest rate, the number of compounding periods per year, and the time in years. Common compounding frequencies include annually, semi-annually, quarterly, monthly, and daily. The Effective Annual Rate (EAR) is used to express the actual annual return accounting for compounding frequency, calculated as . Continuous compounding is the limiting case where compounding frequency approaches infinity, calculated by . Compound interest grows investments faster than simple interest by earning interest on accumulated interest as well as the principal. Understanding compound interest is critical for evaluating the true future value of cash flows, comparing investment options, and accurately assessing costs in project financing, depreciation, and loan amortization. This knowledge helps prevent errors in budgeting and lifecycle cost estimation in engineering projects.