Definition of Compound Interest
Compound interest is the process by which interest is added to the principal amount invested or borrowed, and then, in subsequent periods, interest is earned or charged on the original principal plus the previously accumulated interest. This creates a snowball effect, where the amount grows exponentially over time, unlike simple interest which only applies to the initial principal.
Key Principles and Formula
The core principle of compound interest relies on the frequency of compounding and the interest rate. The standard formula is A = P(1 + r/n)^(nt), where A is the amount after time t, P is the principal, r is the annual interest rate (decimal), n is the number of compounding periods per year, and t is the time in years. This formula accounts for how interest accumulates periodically, amplifying growth.
Practical Example
Consider investing $1,000 at an annual interest rate of 5% compounded annually for 10 years. Using the formula, A = 1000(1 + 0.05/1)^(1*10) = 1000(1.05)^10 ≈ $1,628.89. If compounded monthly (n=12), the amount grows to approximately $1,647.01, demonstrating how more frequent compounding increases the final value.
Importance and Applications
Compound interest is crucial in personal finance for building wealth through savings accounts, retirement funds like 401(k)s, and investments such as stocks or bonds. It rewards long-term saving by accelerating growth, but for borrowers, it can increase debt if payments are not made promptly. Understanding it helps in making informed decisions about loans, mortgages, and investment strategies.