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Last updated on June 12th, 2025

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Difference Between Simple Interest and Compound Interest

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Interest is the amount of borrowing money or the earnings on deposits. Simple interest is a method of calculating interest on an initial investment amount. For every time period, the interest rate remains constant. Whereas, compound interest is an approach to calculating the interest rate on both the principal amount and the interest earned previously. In this topic, we will explore simple interest and compound interest.

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Difference between Simple Interest and Compound Interest

Simple interest (SI) remains unchanged over time, which is earned or paid on the original principal amount. This type of interest is used in loans such as student loans, installment loans, car loans, and so on. While the compound interest (C.I.) allows the money to increase faster over time.

 

This type of interest is used in investments and savings accounts. The interest rate of compound interest is higher than the interest rate of simple interest. Let us look at an example to understand this better. Suppose you deposit money in a bank and the interest rate is 2% per year. With simple interest, the money increases at a fixed rate. While with the compound interest, the investment amount grows faster beyond our expectations.

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Formula for Simple Interest and Compound Interest

The two main types of interest are simple interest (S.I) and the compound interest (C.I). Knowing the difference between the two types of interest and their formulas helps us make better financial decisions. The formulas of simple interest and compound interest are:

 

Simple interest = SI =  P × R × T / 100

 

Compound interest = A = P (1 + R / 100n)nT 

 

Now, let us understand the variables:
P = Initial amount
R = Rate of interest 
T = Time duration
N = Number of times interest is compounded per year

 

Knowing these formulas will help increase earnings and minimize our debts by ensuring accurate calculations. By understanding the concepts of interest rates we can optimize our investments, manage the costs, evaluate the loan and repayment strategies. 

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Properties of Simple Interest and Compound Interest

To plan financial transactions, borrowings, and investments, we need to understand the properties and significance of simple interest and compound interest. Understanding the properties of both types of interest helps us make smarter financial decisions. It will help us to choose the best savings options and investing plans. The properties of simple interest are listed below:

  • The interest rate of simple interest is fixed which is calculated on the initial principal amount. 

 

  • The growth of the amount is linear and at a constant rate over the period.

 

  • The duration and the interest rate are inversely related.

 

  • Commonly used in personal loans, installment loans, car loans and for short-term borrowings. 

 

The following is the list of properties of compound interest:

  • Compound interest is referred to as interest on interest. Each time the interest is added, the compound interest is calculated on the original and the accumulated interest. 

 

  • The growth of the amount is faster over time.

 

  • Commonly used in investments, fixed deposits, savings accounts, and for long-term investments.

 

  • The more often interest is added such as daily, monthly, or yearly, the total money increases quickly. 
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Importance of Simple Interest and Compound Interest for Students

In our daily lives, we need to manage money more efficiently and plan for the future financial operations. Understanding the concepts of simple interest and compound interest is crucial for students to know how interest and money management work and to choose the right investment options. 

 

  • Students can comprehend how interest functions in investments, loans, and savings. They will learn about financial literacy and capital management skills. 

 

  • Students who take education loans for their studies can become aware of how to pay back their loans to avoid future financial troubles.

 

  • They can select the best investment possibilities that will teach them about the vast benefits of compound interest. 

 

  • Students  can compare different loan types, interest rates, credit cards, and savings accounts at their younger age.

 

  • To plan for a financially independent future, the simple interest and compound interest concepts help the kids by ensuring financial security.  
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Advantages and Disadvantages of Simple Interest and Compound Interest

Simple interest and compound interest have their own merits and demerits, making them vital in financial decision-making. Simple interest is best for short-term financial operations, while compound interest is more beneficial for long-term investments. 


Advantages of simple interest:

 

  • The calculation of simple interest is easy and straightforward. 

 

  • The interest amount remains unchanged over the time period, helping to predict the payments.

 

  • It reduces the financial burden on borrowers because the interest rate for loans is lower, as it is calculated only on the initial amount. 

 

  • Simple interest is best for short-term loans, education loans, car loans, and other borrowings. 

 

  • The payment schedules of loans with simple interest are easier to understand and they have clear terms. 

 

Disadvantages of simple interest:

 

  • The simple interest rate earned on savings and investments is lower than the compound interest.

 

  • It is not suitable for long-term investment because the interest rate is constant over time.

 

  • Money does not grow significantly, making it less beneficial for investors.

 

Advantages of Compound Interest:

 

  • The interest is earned on both the principal amount and the accumulated interest, resulting in rapid growth of money.

 

  • Compound interest is beneficial for long-term investments and gives higher returns for lenders and investors.

 

  • It is commonly used in fixed deposits, mutual funds, and real estate investments. 

 

Disadvantages of Compound Interest:

 

  • If loans with compound interest are not managed properly, they can create financial burden for the borrowers.

 

  • The calculation and the formula for compound interest are complex and can be difficult to understand. 

 

  • In long-term investments, money growth takes time and requires patience. 
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Common Mistakes and how to avoid them in Simple Interest and Compound Interest

Simple interest and compound interest are the fundamental concepts in mathematics and finance. It teaches students how to manage money effectively by reducing future financial risks. However, mistakes in the calculation of simple interest and compound interest can lead to incorrect results and other problems. Here are some of the common errors and its helpful solutions to avoid them:
 

Mistake 1

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Using the incorrect formula
 

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Always check for the correct formula. Sometimes, students may get confused about the formulas of simple interest and compound interest. The correct formula of simple interest is:


SI =  P × R × T / 100


Then, the correct formula for compound interest is:


 A = P (1 + R / 100n)nT 

Mistake 2

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Neglecting the time period
 

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Check if the time period is given in months or years. If the time duration is provided in months, students should convert it to years by dividing by 12.

 

For example, if you deposit $2000 in a bank at an annual interest rate of 10% for 24 months using simple interest. To find the answer, we have to convert the months to years.
24 months = 24 / 12 = 2 years. 
Like this, we have to convert months to years before using the formula. 
 

Mistake 3

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Failing to add interest to principal in the final calculation
 

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To find the final amount, use A = P +SI. Some kids only calculate SI but forget to add it to the original amount (principal, P), which will lead to wrong calculation. They will get the correct total amount by adding the interest to the principal.
 

Mistake 4

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Incorrectly positioning decimal points in percentage calculations

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Before using the given interest rate in the formula, always remember to divide it by 100. Students forget to convert the interest rate from percentage to decimal.

 

For example, if the given interest rate is 4%. Convert it by dividing 4 by 100. It gives 0.04. So, use 0.04 instead of 4%. 

Mistake 5

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Applying the annual formula to quarterly or monthly compounded interest
 

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According to the compounding periods per year, modify the formula for ‘n’. The formula for compound interest is:
A = P (1 + R / 100n) nT 
Here, the n is the number of compounding periods per year. So the value for annual compounding is 1.
Semi- annually =2 
Quarterly = 4
Monthly = 12 
Daily = 365
Therefore, according to the given periods per year, we have to modify the value of ‘n’. 

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Solved Examples for Simple Interest and Compound Interest

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Problem 1

Tom bought a house worth $50,000 and borrowed money from a bank at 5% simple interest per year for 10 years. Calculate the total amount he has to pay back after the period.

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$75,000
 

Explanation

To find the answer, we will use the simple interest formula, because the interest rate is fixed. 

SI =  P × R × T / 100

Here, P= $50,000

R = 5%

T = 10 years

Let us substitute the values:

SI = 50,000 × 5 × 10 / 100 

50,000 × 5 × 10 = 2,500,000

2,500,000 / 100 = 25,000

So, the simple interest is $25,000

Next, we can find the total amount to be paid back after 10 years:

Total amount = P + SI

50,000 + 25,000 = 75,000

Therefore, Tom has to repay a total of $75,000 to the bank after 10 years. 

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Problem 2

Sara borrowed $45,500 for 24 months at 10% per annum. Find the simple interest she will need to pay.

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$9100
 

Explanation

The formula for finding the simple interest is:


SI =  P × R × T / 100


Here, P= $45,500


R = 10%


T - 24 months


Here, we need to convert 24 months into years.


24 / 12 = 2 years


Now, we can substitute the values:


SI = 45,500 × 10 × 2 / 100 


910000 / 100 = 9,100


Therefore, the simple interest Sara needs to pay is $9,100. 

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Problem 3

How much money was invested at 4% annual simple interest for 4 years to earn $36,000?

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$225,000
 

Explanation

Here, SI = $36,000

R = 4%

T = 4 years

We have to find the principal amount (P);

So, the formula will be like:

P = SI × 100 / R × T 

P = 36,000 × 100 / 4 × 4

3,600,000 / 16 = 225,000

Hence, to earn $36,000 in interest at 4% per year over 4 years, the initial payment was $225,000. 

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Problem 4

Miya lends $2000 to Eliz at an interest rate of 5% per annum, compounded half-yearly for a period of 2 years. Find how much amount she gets after a period of 2 years from Eliz.

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$2207.60

Explanation

Here, the interest is compounded half-yearly. So, the formula will be:

 A = P (1 + R / 100n) nT 

Where, P = $2000

R = 5%

T = 2 years

n = 2 (half-yearly)

Let us substitute the values to the formula:

A = 2000 (1 + 5 / 100 × 2) 2× 2 

A = 2000 (1+ 5 / 200) 4

A = 2000 (1 + 0.025) 4 = 2000 × (1.025) 4

(1.025) 4 = 1.1038 

So, A = 2000 × 1.1038 = 2207.60

Therefore, Miya will receive $2207.60 from Eliz after 2 years. 

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Problem 5

Loki invests $6000 in a savings account with an annual interest rate of 3% compounded annually. How much will he have after 3 years?

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$6556.36
 

Explanation

The interest is compounded annually, so the formula will be:

A = P (1 + R/100) T

Here, P = $6000

R = 3%

T = 3 

Now, we can substitute the values:

A = 6000 (1 + 3 / 100) 3

A = 6000 (1.03)3

(1.03)3 = 1.092727

Next, multiply by the principal (P):

A = 6000 × 1.092727

A = 6556.36

Hence, after 3 years, Loki will have $6556.36 in his savings account. 

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FAQs on Simple Interest and Compound Interest

1.What is simple interest?

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2.What is compound interest?

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3.Can compound interest be considered as income?

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4.What makes compound interest so important?

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5.When is simple interest and compound interest beneficial?

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Dr. Sarita Ghanshyam Tiwari

About the Author

Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo

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