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Interest plays a crucial role in finance, determining the cost of borrowing and the return on investments. Simple interest is calculated on the principal alone, while compound interest grows exponentially by earning interest on accumulated interest. This text explores the formulas for both, their applications in real-world scenarios, and their significance in financial decision-making. Understanding these concepts is key for managing loans, savings, and investment strategies effectively.

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## Definition of Interest

### Key element in finance

Interest is a crucial factor in finance, representing the cost for borrowing or the return on investment

### Calculation of Simple Interest

Formula for simple interest

Simple interest is calculated using the formula I = PRT, where I is the interest, P is the principal, R is the annual interest rate, and T is the time in years

Application of simple interest

Simple interest is typically used for short-term loans or investments, where interest is not compounded at regular intervals

### Calculation of Compound Interest

Formula for compound interest

Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years

Impact of compound interest

Compound interest can lead to exponential growth, especially over long periods, due to the effect of earning "interest on interest."

## Application of Interest

### Borrowing

Interest is applied to borrowing, where the borrower pays the lender a percentage of the principal as a cost for using the borrowed funds

### Investing

Interest is also applied to investments, where the investor earns a return on their initial capital as a reward for their investment

### Savings

Interest is also applied to savings, where the bank pays the depositor interest on their initial deposit, increasing its value over time

## Types of Interest

### Simple Interest

Simple interest is calculated on the principal amount alone and does not compound

### Compound Interest

Compound interest is calculated on the principal amount as well as on the accumulated interest of previous periods, leading to exponential growth over time

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