Difference Between Simple Interest and Compound Interest Explained

The main difference between simple interest and compound interest is how the interest is calculated. In simple interest, the interest is always calculated only on the original amount (called the principal). It stays the same for each time period. But in compound interest, the interest is calculated on both the principal and the interest earned in previous periods. This means the amount grows faster with compound interest because each year you earn interest on a bigger amount. So, simple interest stays steady, while compound interest keeps increasing over time.

What is Simple Interest?

Simple interest is a basic way of calculating how much extra money you earn or pay on a certain amount of money (called the principal) over a period of time. In simple interest, the interest is always calculated only on the original amount you started with, not on any interest earned before. This means that the rate of interest and the time stay the same throughout. For example, if you borrow or invest ₹1,000 at a 5% rate of interest per year, you will earn or pay ₹50 each year. The amount doesn’t change because the interest is not added back to the principal. This method is easy to understand and is commonly used in schools, banks, and simple loan agreements. The formula used to calculate simple interest is:

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Simple Interest = (Principal × Rate × Time) ÷ 100

Compound interest is the interest you earn not only on the original amount of money (called the principal) but also on the interest that gets added over time. This means the interest keeps increasing because it is calculated on a growing total. For example, if you invest ₹1,000 at a 10% rate, you get ₹100 after the first year. In the second year, the interest is calculated on ₹1,100 instead of ₹1,000. So, you earn more each year. This process of earning "interest on interest" helps your money grow faster compared to simple interest.

What is the Difference Between Simple Interest and Compound Interest

The important difference between simple and compound interest are as follows:

Simple Interest	Compound Interest
S.I. can be assumed as the amount that is returned for using the accepted money, over a fixed duration of time. It is always calculated on the initial principal amount every time.	C.I. as per the name is the interest added to the collective interest of previous years, leading the borrowers to pay interest on interest along with the principal.
As the calculation involves a fixed amount, the return amount in simple interest is much lower.	When compared to S.I. the return is much higher as the interest keeps on increasing every year.
Simple interest is assigned only on the loan quantity i.e. the principal amount is constant here.	Compound interest is set and computed on the loan amount + accumulated interest. This indicates that the principal amount is constantly changing throughout the borrowing duration.
There is steady growth in the wealth as the interest is charged on the principal amount.	The wealth growth is exponential in this case as the interest is charged on the principal plus the accumulated interest.

Difference Between Simple Interest and Compound Interest Formula

Simple Interest Formula

The simple interest formula can be calculated using:

Here,

“P” is the principal amount or the initial amount invested or borrowed from the bank.

“R” is the rate of interest at which the principal amount is shared with an individual for a certain time.

“T” is the time duration for which the principal amount is given to an individual.

Applications of Simple Interest

Simple interest is used in many everyday financial products, such as:

• Short-term loans: Used for personal loans, small business loans, and some home loans. The interest is easy to calculate and stays the same over time.
• Savings accounts: Some bank savings accounts give interest based on the simple interest formula.
• Bonds: Certain types of bonds pay interest using simple interest, meaning the interest is only calculated on the original amount you invested.

Compound Interest Formula

The compound interest formula can be calculated using:

CI = A – P

Where A is the amount and is calculated by the formula:

Hence, the final C.I. formula is:

For the above two formulas:

‘A’ stands for the amount.

‘P’ is the principal.

‘R’ denotes the rate of interest.

‘T’ is the time in years

Applications of Compound Interest

Compound interest is used in many financial products to help money grow faster. Here are some common uses:

Savings Accounts: Your savings grow over time because you earn interest on both the money you put in and the interest that’s added.

Investments: In things like stocks, mutual funds, and retirement plans, compound interest helps your money grow more and more over time.

Home Loans (Mortgages): Compound interest is used to calculate how much you owe on a home loan. Managing it well helps avoid extra debt.

Retirement Accounts: These accounts grow faster because your contributions and the interest earned are reinvested, giving you more money in the future.

What is an interest rate?

Interest rate is the additional amount that the individual pays whenever they borrow some money from a bank or any other source at the time of return. The interest charged can be either simple interest or compound interest.

Some Important Formulas for difference between Simple Interest and Compound Interest

The difference between compound and simple interest for two years can be determined using the below formula:

This can also be written as,

The difference between compound and simple interest for three years can be determined using the below formula:

This can also be written as:

For both formulas; P is the principal amount and R is the rate of interest.

Difference Between Simple Interest and Compound Interest Solved Examples

The idea of S.I. is the amount spent for the capital borrowed for a specified time. On the other hand in compound interest, the interest every time is added back to the principal amount.

Let us step toward some solved examples to understand simple interest vs compound interest.

Solved Example 1: What is the difference between simple interest and compound interest for two years if the principal amount is Rs 1000 and the rate of interest is 10%?

Solution:

Given data:

T = 2 years

P = Rs. 1000

R = 10%

Method 1:

⇒

⇒ Rs. 210

⇒

⇒ Rs. 200

Difference = CI – SI = 210 – 200

Difference = Rs 10.

∴ The difference between compound interest and simple interest CI and SI for 2 years is Rs. 10.

Method 2:

The difference between simple and compound interest can also be calculator directly by the formula:

The difference between compound interest and simple interest for 2 years=10

Solved Example 2: If the difference between S.I. and C.I. at a 10% per annum rate of interest for 3 years is Rs. 930, then find the principal value.

Solution:

Given:

Rate of interest = 10%

Time = 3 years

Difference between compound interest and simple interest for 3 years = Rs. 930

The formula used is:

After solving we get:

P =30,000

Solved Example 3: The difference between compound interest and simple interest for 3 years is Rs. 616 at 8% per annum. Obtain the value of the compound interest in 2 years at the same rate of interest at the same sum.

Solution:

Given that for 3 years, the difference between simple interest and compound interest = Rs. 616

Rate = 8%

Therefore P can be obtained through the formula:

⇒

⇒

⇒

⇒ Rs. 31,250

Now:

⇒

⇒

⇒

⇒ Rs. 5200

∴ The C.I. in two years at the same rate of interest at the same sum is Rs. 5200.

Solved Example 4:The difference between simple interest for one year and compound interest for the half year on Rs. 1200 at 10% per annum is?

Solution:

P = Rs. 120

For calculating the compound interest,

Principal = Rs. 1200

Time period = two years

Rate = 10/2 = 5%

=

= Rs. 123

Therefore the difference = CI – SI = 123 – 120 = Rs. 3

∴ The difference between simple interest for one year and compound interest for the half year on Rs. 1200 at 10% per annum is Rs. 3

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If you are checking the Difference between Simple Interest and Compound Interest article, also check the related maths articles in the table below:
What is Interest	Simple Interest
Compound Interest	Profit Formula
Simple Interest MCQs	Compound Interest MCQs

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