Difference Between Simple Interest and Compound Interest Formula

Difference Between Compound Interest and Simple Interest Formula - Many students wonder what is the difference between simple interest and compound interest. But once they know the meaning and formulas, understanding the difference between CI and SI becomes easy to learn. 

Simple interest (SI) means the extra money is added only to the main amount (which is called Principal Amount). On the other hand, Compound Interest (CI) means the extra money is added on both the principal and also on the interest that was already added before. To understand the key difference between simple interest and compound interest formula, keep reading.

Difference Between Simple and Compound Interest With Examples

Here we will learn about what is the difference between simple interest and compound interest and difference between SI and CI formula:

Simple Interest is the extra money given only on the original amount, which is called the principal. This interest stays the same, no matter how much longer one keeps their money in the bank.

• For example, if you keep INR 1,000 in your bank account and the bank gives 10% interest, then every year you will get INR 100 in the form of interest. Therefore, Simple interest is easy to understand and is mostly used in small loans or savings where the interest amount stays fixed.

Compound Interest is a little different because here the interest is added on the principal as well as on the interest already earned. This means, every year, the total amount keeps increasing, and the next year’s interest is calculated on the new, increased amount. So, the interest keeps increasing faster.

• For example, if you keep INR 1,000 in your bank with compound interest, the first year you'll get INR 100, but next year, interest is given at INR 1,100 (INR 1,000 (Principal) + INR 100 (interest earned in the previous month)). Compound interest is used in many types of bank accounts and investments.

Compound and Simple Interest Formulas Overview

To understand the difference between SI and CI formula, it is important to know how simple and compound interest work to calculate the interest (extra money) that is added. Find out the easy explanation of SI and CI formula here:

1. Simple Interest Formula (SI)

The formula for simple interest is: SI = P × R × T ÷ 100.
Where:

• P is the principal or the original amount of money.

• R is the rate of interest or the percentage of money added every year.

• T is the time (in years).

This SI formula shows how the same amount of interest is added every year on the principal amount.

2. Compound Interest Formula (CI)

On the other hand, the formula for compound interest is a little different than simple, which is: CI = P × (1 + R/100)^T - P. In this formula of compound interest:

• P is the principal or the original amount of money.

• R is the rate of interest or the percentage of money added.

• T is the time (in years).

Read More: Unit Fraction

What is the Difference Between CI and SI Formula?

The difference between CI and SI formulas is easy to understand when we look at how interest is added. In simple interest, the same amount of interest is added every year on the original amount, called the principal. But in compound interest, the interest is added not just on the principal but also on the interest earned before, making the amount increase over time. This is the reason why compound interest is used for saving money, while simple interest is used for loans.

Difference Between CI and SI Formulas With Examples

To know how simple interest (SI) and compound interest (CI) work, let us revise their formulas to how to calculate simple interest and apply them in an example.

As learned above, the SI formula is: SI = (P × R × T) ÷ 100, where P is the principal (starting money), R is the rate of interest, and T is the time in years. The CI formula on how to calculate compound interest is CI = P × (1 + R ÷ 100)ᵗ – P, which shows how CI adds interest on both the principal and the interest earned before. Let’s take an example now to understand the difference between CI and SI formulas:

Suppose you have INR 1,000 kept for 2 years at a 10% interest rate in your bank account:

• Using the Simple Interest (SI) formula: SI = (1000 × 10 × 2) ÷ 100 = INR 200

• Using the Compound Interest (CI) formula: CI = 1000 × (1 + 10 ÷ 100)² – 1000 = 1000 × (1.1)² – 1000 = 1210 – 1000 = INR 210

These examples show that with compound interest, you get more money compared to simple interest for the same time period and rate of interest.

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Relation Between Simple Interest and Compound Interest

Now it can be said that Simple interest (SI) and compound interest (CI) both can be used for calculating how much extra money one can get when they keep their money in a bank or give it to someone for some time. The main difference is that SI is calculated only on the principal amount, while CI is calculated on the principal amount plus the interest earned before.

Let’s understand this with an easy example:

Seema has INR 2,000, which she wants to keep deposited for 2 years to earn some extra money on it. For that, she checks two banks:

• Bank A gives Simple Interest (SI) at 5% per year.

• Bank B gives Compound Interest (CI) at 5% per year.

Let’s help how to calculate compound interest and how to calculate simple interest where she will get more money after 2 years.

While both banks gave extra money, Bank B gave INR 5 more because it used compound interest. This means that compound interest helps money grow faster than simple interest, even when the interest rate and time are the same.

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