Compound Interest

Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It differs from simple interest, which is calculated only on the principal amount.

Components of Compound Interest

Compound interest involves several key components that influence how the total amount grows over time.

• Principal (P): The initial sum of money invested or borrowed.
• Interest Rate (r): The percentage at which the principal earns interest, usually expressed annually.
• Time (t): The duration for which the money is invested or borrowed, usually expressed in years.
• Number of Compounding Periods (n): The frequency with which interest is applied to the principal (e.g., annually, semi-annually, quarterly, monthly).

Calculation of Compound Interest

The formula for calculating compound interest is:

A = P (1 + r/n)^(nt)

Where:

• A: The total amount after interest.
• P: The principal amount.
• r: The annual interest rate (decimal).
• n: The number of times interest is compounded per year.
• t: The number of years the money is invested or borrowed.

Example of Compound Interest calculation

1. Let’s say you invest $1,000 (P) at an annual interest rate of 5% (r) compounded annually (n = 1) for 10 years (t).
2. Using the formula: A = 1000 (1 + 0.05/1)^(1*10)
3. Calculating: A = 1000 (1 + 0.05)^(10) = 1000 (1.05)^(10) ≈ 1000 * 1.62889 ≈ $1,628.89.

Summary

Compound interest significantly enhances the growth of investments because it allows earned interest to generate additional interest over time. This results in exponential growth compared to simple interest. Understanding compound interest is vital for effective financial planning and investment strategies.