Overview of Simple and Compound Interest
Simple interest is calculated only on the initial principal amount, resulting in linear growth over time. In contrast, compound interest is calculated on the principal plus any accumulated interest, leading to exponential growth. The primary difference lies in the base amount used for interest computation: simple interest uses just the original sum, while compound interest includes reinvested earnings.
Calculation Methods
Simple interest follows the formula I = P × r × t, where I is interest, P is principal, r is the annual interest rate, and t is time in years. Compound interest uses A = P(1 + r/n)^(nt), where A is the amount after time t, n is the number of compounding periods per year. This compounding effect makes compound interest grow faster, especially with frequent intervals like monthly or daily.
Practical Example
Consider a $1,000 principal at 5% annual interest over 3 years. Simple interest yields $150 total interest ($1,000 × 0.05 × 3), for a final amount of $1,150. With annual compounding, the amount grows to $1,157.63 ($1,000 × (1 + 0.05)^3), adding $57.63 in interest from the compounded portion. This illustrates how compound interest accelerates wealth accumulation.
Applications and Importance
Simple interest is commonly used in short-term loans or bonds due to its straightforward calculation, minimizing complexity. Compound interest powers savings accounts, investments, and long-term loans like mortgages, where it can significantly increase costs or returns over time. Understanding the difference helps in choosing financial products: simple for predictable costs, compound for maximizing growth in savings.