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Compound interest is a fundamental concept in finance that involves earning interest on both the initial principal and the accumulated interest from previous periods. This article delves into the mechanics of compound interest, how it differs from simple interest, and provides examples of how to calculate it using a formula or a table. Understanding compound interest is crucial for anyone looking to maximize investment returns or manage debt over time.

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## Definition of Compound Interest

### Explanation of Compound Interest

Compound interest is the addition of interest to the principal sum of a deposit or loan, where each interest payment may earn further interest

### Comparison to Simple Interest

Definition of Simple Interest

Simple interest is calculated solely on the principal amount for the entire duration of the investment or loan, without compounding

Differences between Compound and Simple Interest

Distinguishing between simple and compound interest is vital for informed financial decision-making, as they can have markedly different impacts on the total amount of interest accrued or paid over time

### Importance of Understanding Compound Interest

A thorough understanding of compound interest is advantageous for anyone engaged in investing or borrowing

## Computation of Compound Interest

### Formula for Compound Interest

The general formula for compound interest is A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount, 'r' is the annual interest rate (decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested or borrowed for, in years

### Alternative Method of Calculation

An alternative method involves constructing a table to calculate the interest for each compounding period and adding it to the principal, which is then used for the next period's calculation, continuing until the total time has elapsed

### Examples of Compound Interest Calculation

Examples of compound interest calculation using both the formula and table method are provided, showing that both approaches yield the same end result

## Components of Compound Interest

### Principal

The principal is the initial amount of money put into the investment or borrowed, and as interest compounds, it is added to the principal, increasing the base for future interest calculations

### Interest Rate

The annual interest rate is a crucial component in the calculation of compound interest, as it determines the amount of interest earned or paid

### Compounding Frequency

The compounding frequency, or the number of times interest is calculated and added to the principal per year, also plays a significant role in the growth of compound interest