# Difference Between Simple Interest and Compound Interest

Compound interest is often called a marvel by Albert Einstein, who famously said, "Those who get it, earn it; those who don't, pay it." Interest is a fee you pay to borrow money from a lender. It's a percentage of the original amount borrowed and is usually paid regularly, like every month or year. There are two main types of interest: simple and compound.

It's crucial to grasp the distinction between these types because it can greatly affect how much you ultimately pay on a loan or earn on an investment.

**Also Check: Diffrence Between area and Volume | Diffrence Between Cube and Cuboid | Diffrence Between Mean, Median Mode**

## Introduction

Interest is like the fee you pay when you borrow money or the earnings you get when you lend money to someone else. It's basically the cost of using someone else's money. When you borrow money, you pay interest to compensate the lender for letting you use their money and for the risk they take. This also means they can't use that money for other things while it's lent out.

Interest is usually shown as a percentage of the amount borrowed or invested, and it's calculated over a certain period of time. There are two main types: simple interest, which is based only on the initial amount borrowed or invested, and compound interest, which includes interest on both the initial amount and any previously earned interest. Understanding these types helps you make smarter choices with your money and get the most out of your investments.

## Understanding Simple Interest and Compound Interest:

**Simple Interest:** Simple interest is calculated based only on the original amount you borrowed or invested, known as the principal. The interest is a percentage of this principal amount. The formula for calculating simple interest is:

Simple Interest=Principal×Rate×Time/100\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} / 100Simple Interest=Principal×Rate×Time/100

For example, if you borrow Rs. 100 at an interest rate of 5% for one year, the simple interest would be Rs. 5.

**Compound Interest:** Compound interest takes into account both the principal amount and the interest that accumulates over time. The interest is added back to the principal at regular intervals, so you earn interest on the interest. The formula for compound interest is:

Compound Interest=Principal×(1+Rate100)n−Principal\text{Compound Interest} = \text{Principal} \times \left( 1 + \frac{\text{Rate}}{100} \right)^n - \text{Principal}Compound Interest=Principal×(1+100Rate)n−Principal

Here, nnn represents the number of times interest is compounded each year. For instance, if you invest Rs. 100 at a 5% interest rate compounded annually for 10 years, your investment would grow to Rs. 162.89.

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## Difference between Simple Interest and Compound Interest

Parameters |
Simple Intrest |
Compound Intrest |

Calculation |
Simple interest is obtained or given only on the principal amount. |
The principal and cumulative interest are used to compute compound interest. |

Formula |
SI=PRT100 |
CI=P(1+r100)n-P |

Time |
Simple interest is calculated only on the actual principal. |
compound interest compounds over time, earning interest on the accumulated interest as well. |

Amount |
Simple interest results in a lower overall interest payout compared to compound interest. |
compound interest compounds over time and earns interest on the accumulated interest. |

Complexity |
Simple interest is considered less complex to calculate than compound interest. |
Compound interest is considered more complex to calculate than simple interest as it takes into account the accumulated interest over time. |

Return amount |
When compared to compound interest, the return is significantly smaller. |
The return is significantly more. |

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## Application of Simple Amount Interest

Simple interest and compound interest are two ways money grows over time.

Simple interest is used for short-term loans like personal loans or car loans. The interest rate stays the same for the whole loan time.

Compound interest is for long-term investments like savings accounts or retirement funds. The interest rate can change and adds to the original amount, making the total grow faster.

Let's see some examples:

Example 1: You borrow Rs. 10,000 at 5% interest for 2 years.

- Simple Interest = Rs. 10,000 x 5% x 2 years = Rs. 1,000
- Compound Interest = Rs. 10,000 x (1 + 5%/100)^2 - Rs. 10,000 = Rs. 1,025

Example 2: If you invest Rs. 5,000 for 10 years at 10% interest per year.

- Amount = Rs. 5,000 x (1 + 10%/100)^10 = Rs. 12,970

So, compound interest grows your money faster over time compared to simple interest. Understanding these helps you decide better about loans and investments to get more returns.

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## Frequently Asked Questions on Difference Between Simple Interest and Compound Interest

Difference = **3 x P(R)²/(100)² + P (R/100)³**

**Compound interest is better for you if you're saving money in a bank account or being repaid for a loan**.

With simple interest, you add 5% of $100 every year, which is $5. Over 10 years, this adds up to $50 in total interest. So, after 10 years, you'd owe $150 in total. With compound interest at 5% annually, you calculate 5% of the amount each year, including the interest that has already built up.

Simple interest is calculated based on the original amount of a loan. It stays the same over time. Compound interest, on the other hand, is calculated on both the original amount and the interest that builds up over time. This means you earn interest on your interest as well.