Education

Simple Interest and Compound Interest – Differences with Examples

One of the main concepts as students one should learn in mathematics is interest. This is because this concept is widely used in the real-life as well. So in this article, we will have a look at the two crucial interest calculation methods- simple interest and compound interest. We will know about the meaning, simple and compound interest formulas, examples, differences and applications to get a clear idea about them.

What is Interest?

  • Whenever a person borrows money for a specific period, he pays some money to use the borrowed money. 
  • This additional amount which he pays to use that money is called interest. 
  • The person who borrows the money pays interest at a pre-decided rate of interest for a specific period. 
  • The person who has given the money will periodically receive this interest amount. 
  • So, interest is the income for the person who lends the money, and it is an extra cost to the person who borrows money.

What is the meaning of Simple Interest?

  • Simple Interest is the interest paid or received on a base amount at a particular interest rate for a specific period. 
  • The base amount is called the principal amount. 
  • Since the interest is calculated on the principal amount, it remains the same throughout the period. 

What is the meaning of Compound Interest?

  • Compound Interest is the interest calculated on the base amount and the interest earned on the previous period. 
  • The base amount is called the principal amount. 
  • Here the benefit of earning interest on interest is gained. 
  • This is more widely used in the real world.

Simple Interest Formula

SI= P*T*R/100

Here, 

SI= Simple Interest

P= Principal Amount

T= Term (Period)

R= Rate of Interest

Total Amount= P I

Compound Interest Formula

CI= P (1 R/100)–P

Here,

CI= Compound Interest

P= Principal Amount

T= Term (Period)

R= Rate of Interest

Amount = Principal (1 R/100)T

Example of Simple Interest

To better understand how to calculate simple interest, let us solve a few examples.

  1. Mr A has taken a loan from Mr B of Rs.1,00,000/- for two years. The interest is 10%. Find the amount to be paid as interest for two years and the total amount paid by Mr.A.

Solution:

In the given case, 

P= 100000

T=2

R=10

To find= SI (Simple Interest)

Formula: Simple Interest= P*T*R/100

Answer:

Inputting the values in the formula, 

SI= 100000*2*10/100= 20000

Conclusion:

The amount of Simple Interest to be paid for two years is Rs.20000/-.

Total Amount= 100000 20000= Rs.120000/-

2. Mr C has taken a loan from Mr D of Rs.1,00,000/- for two years. After two years, Mr C pays Rs. 120000/-. Find the rate of interest.

Solution:

Given

P= 100000

Amount= 120000

T= 2

To find= R?

Formula:  Simple Interest= P*T*R/100

Answer:

From the given data and formula, we have to find R, but Simple Interest is also not available. So we will first find Simple Interest and then use it in the formula to find R.

Amount= Principal Simple Interest

120000= 100000 Simple Interest

Simple Interest = 20000

Putting all the values in the formula,

20000= 100000 * 2 * R / 100

R= (20000 *100) / (100000*2)

R= 10

Conclusion= The rate of interest is 10%

3. Mr E has taken a loan from Mr F of Rs. 1,00,000/- and Simple Interest was Rs.20000. This loan was taken at the rate of 10%. Find the term of the loan.

Solution:

Given

SI= Rs. 20000

P= Rs.100000

R = 10%

To find: T

Formula: Simple Interest= P*T*R/100

Answer: 

Inputting the values in the formula, 

20000= 100000* T * 10 /100

T= (20000 * 100) / (100000 * 100)

T = 2

Conclusion= The term is of 2 years.

Example of Compound Interest

To better understand how to calculate compound interest, let us solve a few examples.

  1. It was estimated that the population would increase at a rate of 10% every year. The population today is 100000. What would be the population after 3 years?

Solution:

Given: P = 100000the 

T= 3

R= 10

To find: Amount

Formula:  Amount = Principal (1 R/100)T

Answer:

Inputting the values in the formula, 

Amount = 100000 (1 10/100)3

Amount = 133100

Conclusion: The population after three years would be 133100.

  1. It was estimated that the population would increase at a rate of 10% every year. The population today is 100000 and is expected to be 133100 after a few years. Find the number of years in which this increase is going to happen.

 

Given: P = 100000

A= 133100

R= 10

To find: Number of years (T)

Formula:  Amount = Principal (1 R/100)T

Answer:

Inputting the values in the formula, 

133100= 100000 (1 10/100)T

T= 3

Conclusion: The number of years for which the population increase is expected to happen is 3 years.

  1. It was estimated that the population would increase after 3 years. The population today is 100000 and is expected to be 133100 after a few years. Find the rate of interest.

Given: P = 100000

A= 133100

T = 3

To find: Rate of  Interest (R)

Formula:  Amount = Principal (1 R/100)T

Answer:

Inputting the values in the formula, 

133100= 100000 (1 R/100)3

R = 10

Conclusion: The rate of interest is 10%.

Combined Example of Simple Interest and Compound Interest

  1. Mr X has taken a loan from Mr Y of Rs.1,00,000/- for two years. The interest is 10%. Find the amount to be paid as interest for two years and the total amount paid by Mr X using simple interest and compound interest.

Solution:

Simple Interest

In the given case, 

P= 100000

T=2

R=10

To find= SI (Simple Interest)

Formula: 

Simple Interest= P*T*R/100

Compound Interest= P (1 R/100)–P

Answer:

Inputting the values in the formula, 

Simple Interest= 100000*2*10/100= 20000, Total Amount = 100000 20000= 120000

Compound Interest= 100000(1 10/100)– 100000 = 21000, Total Amount= 100000 21000= 121000

Conclusion:

The Simple Interest to be paid for two years is Rs.20000/- and Compound Interest is Rs. 21000/-.

The Total Amount using Simple Interest and Compound Interest is Rs. 120000/- and Rs. 121000/- respectively.

 

Differences between simple interest and compound interest

Simple Interest Compound Interest
1. Simple Interest is calculated on the principal value. 1. Compound interest is calculated on principal value and interest
2. Simple interest remains the same throughout the loan. 2. Compound Interest increases after each period.
3. Simple Interest is less than compound interest as there is no interest on interest 3. Compound Interest is larger than simple interest.
4. SI = P*T*R/100 4. CI= P (1 R/100)–P

Application of Simple Interest

Some of the applications of Simple Interest are as follows:

  1. Borrowing amount for a specific period
  2. Car loans
  3. Equi-monthly instalments (EMIs)

Application of Compound Interest

Some of the applications of Compound Interest are as follows:

  1. Population growth in a country
  2. Depreciation of an asset
  3. Bank interest
  4. Credit Cards
  5. Increase in bacteria

Conclusion

We hope this article makes the concept and calculations of simple interest and compound interest easy for you. With practice, you can easily do well in this topic.

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