# Explain how compound interest is different from simple interest?

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## Introduction

Compound interest and simple interest are two different methods of calculating interest on a loan or investment. While both methods involve earning interest on a principal amount, they differ in terms of how the interest is calculated and added to the principal. In this article, we will explore the differences between compound interest and simple interest, and how they affect the growth of an investment or the cost of borrowing.

## Understanding Simple Interest

Definition: Simple interest is a straightforward method of calculating interest, where the interest is calculated only on the initial principal amount.

When using simple interest, the interest is calculated based on the principal amount and the interest rate. The interest earned remains constant throughout the duration of the loan or investment. For example, if you invest \$1,000 at a simple interest rate of 5% per year, you will earn \$50 in interest each year.

The formula for calculating simple interest is:

Interest = Principal x Rate x Time

Where:
– Principal is the initial amount invested or borrowed
– Rate is the interest rate per time period
– Time is the duration of the investment or loan in the same time units as the interest rate

## Exploring Compound Interest

Definition: Compound interest is a more complex method of calculating interest, where the interest is calculated not only on the initial principal amount but also on the accumulated interest from previous periods.

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With compound interest, the interest earned in each period is added to the principal, and subsequent interest calculations are based on the new total. This compounding effect leads to exponential growth in the investment or debt.

The formula for calculating compound interest is:

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

Where:
– A is the final amount including principal and interest
– P is the principal amount
– r is the annual interest rate (expressed as a decimal)
– n is the number of times that interest is compounded per year
– t is the number of years

## Differences Between Compound Interest and Simple Interest

1. Accumulation of Interest: In simple interest, the interest earned remains constant throughout the duration of the investment or loan. However, compound interest allows for the accumulation of interest, leading to exponential growth.

2. Frequency of Calculation: Simple interest is calculated based on the initial principal amount and remains constant. On the other hand, compound interest is calculated based on the principal and accumulated interest, and the frequency of compounding determines how often the interest is added to the principal.

3. Impact on Growth: Compound interest has a greater impact on the growth of an investment compared to simple interest. As the interest is reinvested or added to the principal, the investment grows at an accelerated rate.

4. Cost of Borrowing: When it comes to borrowing, compound interest can result in higher costs compared to simple interest. As the interest is added to the principal, the outstanding balance increases, leading to higher interest charges over time.

## Conclusion

In summary, compound interest and simple interest are two different methods of calculating interest. Simple interest is based on the initial principal amount and remains constant throughout the duration, while compound interest allows for the accumulation of interest by adding it to the principal. Compound interest has a compounding effect, leading to exponential growth in investments or higher costs of borrowing. Understanding the differences between these two methods is crucial when making financial decisions.

## References

– Investopedia: www.investopedia.com/terms/c/compoundinterest.asp
– The Balance: www.thebalance.com/simple-interest-315436