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    Difference Between Simple Interest and Compound Interest

    The main difference simple interest and compound interest is simple interest is paid on only principal amount whereas compound interest is paid both on principal and interest gained in the previous periods. Learn more at BYJU'S.

    MathsMaths Difference BetweenDifference Between Simple Interest And Compound Interest

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    Difference Between Simple Interest and Compound Interest

    The major difference between simple interest and compound interest is that simple interest is based on the principal amount. In contrast, compound interest is based on the principal amount and the interest compounded for a cycle of the period.

    We know that simple interest and compound interest are the two important concepts widely used in many financial services, especially in banking. Loans such as instalments loans, auto loans, educational loans, and mortgages use simple interest. Compound interest is used by most savings accounts as it pays the interest. It pays more than simple interest. In this article, let us discuss the difference between simple interest and compound interest in detail.

    Definition of Simple and Compound Interest

    Simple Interest: Simple interest can be defined as the principal amount of a loan or deposit a person makes into their bank account.Compound Interest: Compound interest is the interest that accumulates and compounds over the principal amount.

    Check out here: Interest formulas

    Simple Interest Calculator

    Compound Interest Calculator

    What is the Difference between Simple and Compound Interest?

    Below you can find the key differences between Simple Interest and Compound Interest in the tabular column below:

    Simple Interest and Compound Interest Differences

    Parameter Simple Interest Compound Interest

    Definition

    Simple Interest can be defined as the sum paid back for using the borrowed money over a fixed period of time.

    Compound Interest can be defined as when the sum principal amount exceeds the due date for payment, along with the rate of interest for a period of time.

    Formula

    S.I. = (P × T × R) ⁄ 100 C.I. = P(1+R⁄100)t − P

    Return Amount

    The return is much lesser when compared to compound interest.

    The return is much higher.

    Principal Amount

    The principal amount is constant.

    The principal amount keeps on varying during the entire borrowing period.

    Growth

    The growth remains quite uniform in this method.

    The growth increases quite rapidly in this method.

    Interest Charged

    The interest charged on is for the principal amount.

    The interest charged on it is for the principal and accumulated interest.

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    Solved Examples

    Q.1: Amita borrowed ₹50,000 for 3 years at a rate of 3.5% per annum. Find the simple interest.

    Solution: Given, P = Rs 50,000 R = 3.5% T = 3 years

    SI = (P × R ×T) / 100

    SI = (50,000× 3.5 ×3) / 100 = ₹ 5250

    Q.2: The count of a population of men was found to increase at the rate of 2% per hour. Find the count at the end of 2 hours if the initial count was 600000.

    Solution: Since the population of men increases at the rate of 2% per hour, we use the formula

    A = P(1 + R/100)n

    Thus, the population at the end of 2 hours = 600000(1 + 2/100)2

    = 600000(1 + 0.02)2 = 600000(1.02)2 = 624240

    Frequently Asked Questions – FAQs

    What is the main difference between simple interest and compound interest?

    Simple interest is computed on the principal amount or loan amount whereas compound interest is computed based on the principal amount as well as the interest accumulated for a certain period or previous period.

    What is the formula for simple interest?

    The formula for simple interest is given by:

    SI = (P x R x T)/100

    where SI = Simple Interest

    P = Principal Amount

    R = Rate of interest

    T = Time duration in years

    What is the formula for compound interest?

    The formula for compound interest is given by:

    CI = Amount – Principal

    and Amount = P(1+r/n)nt

    What is the formula for the amount if it is compounded annually?

    If the amount is compounded annually, the amount is given as:

    A = P(1+R/100)t Quiz on SI Vs CI

    Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

    Select the correct answer and click on the “Finish” button

    Check your score and answers at the end of the quiz

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    Difference Between Simple Interest and Compound Interest

    Learn about Difference Between Simple Interest and Compound Interest topic of Maths in details explained by subject experts on vedantu.com. Register free for online tutoring session to clear your doubts.

    Difference Between Simple Interest and Compound Interest

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    What is Simple Interest and Compound Interest?

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    In this article we are going to be about Simple Interest and Compound Interest. It covers the important topics like Simple Interest and Compound Interest and Simple Interest vs Compound Interest.

    Simple Interest:

    In Mathematics, Simple Interest is a quick and easy method of calculating the interest charge on a given amount of money or loan.

    We can determine this by Simple Interest multiplying the daily rate of interest by the principal by the number of days (n) that elapse between payments.

    The formula for Simple Interest is ,

    Simple Interest (SI) =

    (P×R×T) 100 (P×R×T)100

    Where, P is equal to the Principal, R is the equal to the Rate of Interest,  T = Time (Period).

    The time is in years and the rate of interest is in percentage (%).

    NOTE : 

    Simple interest is calculated by multiplying the rate of interest by the principal and by the number of days (time period)  that  elapse between  the payments.

    It benefits consumers who pay their loans on time or early every month.

    Auto loans and short-term personal loans are examples of places where Simple Interest is used.

    We can calculate the total amount,  using the following formula:

    Amount = Principal  + Interest

    Where, Amount (A) is equal to the total money paid back at the end of the time period (T)    for which the money was borrowed.

    Compound Interest:

    Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period of time.

    Compound interest is different from the Simple Interest.

    In Simple Interest the interest is not added to the principal while calculating the interest during the next period while in Compound Interest the interest is added to the principal to calculate the interest.

    The formula for Compound Interest is ,

    Compound Interest (CI) =

    Principal (1+ Rate 100 ) n −Principal

    Principal(1+Rate100)n−Principal

    where, P is equal to principal ,  R is equal to rate of Interest,  T is equal to Time (Period)

    The Formula to Calculate the Amount is

    Amount=Principal (1+ Rate 100 ) n

    Amount=Principal(1+Rate100)n

    where , P is equal to Principal ,  Rate is equal to Rate of Interest,  n is equal to the time (Period).

    Applications of Compound Interest:

    Some of the applications of Compound Interest are:

    Increase in population or decrease in population.

    Growth of bacteria.

    Rise in the value of an item.

    Depreciation in the value of an item.

    What is the Difference Between Simple Interest and Compound Interest?

    Besides Simple Interest there is another type of interest known as Compound Interest.

    The major difference between Compound and Simple Interest is that Simple Interest is based on the principal of a deposit or a loan whereas Compound Interest is based on the principal and interest that accumulates in every period of time.

    (Image will be uploaded soon)

    Here’s the Difference Between Simple Interest and Compound Interest in a Tabular Form(SI vs CI)

    Simple Interest Compound Interest

    The Simple Interest is the same for all the years.

    The Compound Interest is different for all the years.

    SI < CI. CI > SI.

    Simple Interest (SI) = (P×R×T)/100

    CI = Principal (1+Rate/100)n - principal

    Relation Between Simple Interest and Compound Interest -

    Here’s the relation between Simple Interest and Compound Interest:

    We already know from the SI vs CI definition that the interest is typically expressed as a percentage, and can be Simple or Compound Interest. Simple interest is generally based on the principal amount of a loan or deposit whereas Compound Interest is based on the principal amount and also on the interest that accumulates on the principal every period. We have already discussed this in the SI vs CI definition.

    Questions to be solved:

    1. Sohan takes a loan of Rs 1000 from the Central bank for a period of one year. The given rate of interest is 10% per annum. Find the interest and the amount Sohan has to pay at the end of one year.

    Ans:  Let’s write down the given information,

    Here, the loan amount = Principal = Rs 1000

    Rate of interest = R = 10%

    Time for which it is borrowed = T = 1 year

    The formula to calculate the Simple Interest for one year,

    Simple Interest (SI) =

    (P×R×T) 100 (P×R×T)100

    Thus, the Simple Interest for a year, (SI) =

    (P×R×T) 100 = (1000×10×1) 100

    (P×R×T)100=(1000×10×1)100

    Now, let’s calculate the amount of money at the end of one year,

    Amount = Principal  + Interest

    The amount that Sohan has to pay to the bank at the end of one  year = Principal + Interest = 1000 + 100 = Rs 1100.

    2. Ram borrowed a sum of Rs 5000 for 2 years at the rate of 3% per annum. Find the interest accumulated on the sum of at the end of 2 years and calculate the total amount.

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    Difference Between Simple Interest and Compound Interest

    The difference between simple and compound interest is, simple interest is calculated on principal amount whereas compound interest is calculated on the principal amount and the interest compounded for a cycle of the period.

    Difference Between Simple Interest and Compound Interest

    The difference between simple and compound interest is, simple interest is calculated on principal amount whereas compound interest is calculated on the principal amount and the interest compounded for a cycle of the period. Loans such as installments loans, educational loans, use simple interest. Compound interest is used while investing as it lets funds grow at a faster rate. Compound Interest pays more interest than simple interest.

    Difference Between Simple and Compound Interest

    Simple interest (S.I.) is the sum paid back for using the borrowed money, over a fixed period of time whereas compound interest (C.I.)is calculated when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. The return amount of simple interest is much lesser as compared to compound interest. On the other hand, the return is much higher in compound interest.

    The difference between the formulas of simple interest and compound interest is:

    Here, P = Principal , R = rate of interest ,T = time duration in years, S.I. = Simple Interest and C.I. = Compound Interest

    S.I. = S.I. = (P × R × T) ⁄ 100

    C.I.= P(1+R/100)t − P

    Let us understand the differences in the calculations of Simple interest and compound interest when the principal is $100 for 3 years with 5 % interest. When the calculation is done with simple interest, the principal remains the same for a particular period of time. When the calculation is done with compound interest the principal is revised. The principal along with the interest accumulated in the first period is calculated as the revised principal. Thus the principal keeps on increasing with compound interest.

    Simple Interest Compound Interest

    At the end of the first year, the SI is $5 At the end of the first year, the CI is $5

    At the end of the second year, the principal taken for calculation is the same $100. SI is $10

    At the end of the first year, the principal is $100+ the interest $5= $105 and CI is $10.25

    At the end of the second year, the principal taken for calculation is the same $100. SI is $15 At the end of the second year, the principal taken for calculation is $105 + $10.25 = $115.25 and the CI is $15.76

    Using the formula, we calculate the same as

    SI = (PRT)/100 = (100 × 5 × 3)/100 = $15

    Using the formula, we calculate the same as:

    CI = P(1+R/100)t − P

    = 100(1 + 5/100)3 - 100

    = 100[105/100]3 - 100

    = 1157625/ 10000 - 100

    =$15.76

    Simple Interest vs Compound Interest

    Look at the image given below which shows the differences between simple and compound interest.

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    Simple Interest and Compound Interest Examples

    Example 1: Find the difference between the simple interest and the compound interest on $5000 for 2 years at 9% per annum.Solution: 

    S.I. = (P × R × T ) ⁄ 100 and C.I.= P(1+R/100)t − P

    Principal = $5000 , Time(t) = 2 years , Rate of interest (r) = 9%

    S.I. = $(5000 × 9 × 2) / 100 = $900

    C.I.= P(1+R/100)t − P = $[5000 (1 + 9 /100)2 -  5000]

    C.I. = $[5940.5 - 5000] = $940.5

    Difference = C.I.- S.I. = $940.5 - $900 = $40.5

    Example 2: Find the simple interest and the compound interest on $2500 for 2 years at 10% per annum.Solution: 

    S.I. = (P × R × T) ⁄ 100 and C.I.= P(1+R/100)t − P

    Principal = $2500 , Time(t) = 2 years , Rate of interest (r) = 10%

    S.I. = $(2500 × 10 × 2) / 100 = $500

    C.I.= P(1+R/100)t − P = $[2500 (1 + 10/100)2 -  2500]

    C.I. = $[3025 - 2500] = $525

    Example 3: Rachel borrows $20000 per annum for 2 years at simple interest and Phoebe borrows the same amount for the same time period at 12% per annum, compounded annually. Who pays more interest and by how much?Solution: 

    Principal (P) = $20000, Time (T) = 3 years, Rate of interest (R) = 12% p.a.

    Simple Interest for Rachel = (P × R × T) / 100 = $(20000 × 12 × 2)/100 = 200 × 12 × 2 = $ 4800

    Compound Interest for Phoebe.= P(1+R/100)t − P  = $[20000 (1 + 12/100)2 - 20000] = $5088

    Difference = C.I.- S.I. = $5088 - $4800  = $288

    Phoebe pays more interest by $288.

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    Practice Questions on Simple Interest and Compound Interest

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