Simple interest

The concepts of simple interest and compound interest are of great importance. In this section, we will learn – simple interest basic concepts and simple interest formula.
I have also included questions based on simple interest concepts.
Make sure you have the knowledge of Percentage and profit and loss from before.

Basic Terms in this concept

Let us understand some terms that we need to know.

1. Principal : The sum of money borrowed or lent is called principal. It is denoted by P.
   
   
2. Time: The time period for which money is borrowed or lent. 
   
   
3. Interest: The amount of  extra money apart from the principal, that we have to pay to the lender is called interest.
   There are two types of interests:
   i) Simple Interest (SI)
   ii) Compound interest (CI)
   It is to be noted that the interest can usually be paid annually, half-yearly and quarterly, depending upon the conditions.
   In this section we will learn simple interest.
   
   
4. Rate percent: It is the rate at which Interest is given. 
   
   
5. Amount: It is the sum of Principal and interest. Or it the the amount we have to pay to the lender including principal and interest.
   Amount = Principal + Interest

For more understanding let us take an example.

Suppose You want to borrow Rs 100 from a person. The person agrees to lend you the money. But If you repay the exact amount to that person after one year, he will have no loss or gain. Then why will he lend the money?

Thus, Interest is added to the borrowed money so that the lender may earn a profit. 
  Have a look at the conversation in the picture. In this case, Rs 100 is the Principal, Rs 10 is the interest, Rs 110 the Amount, and the time duration is 1 year.

Simple Interest Definition

It is usually calculated on the original principal for any duration of time.
Or in other words, the Principal is the same for every year. It is denoted by SI.
Simple interest formula,
     SIMPLE INTEREST (SI) = \frac { P\times R\times T }{ 100 } 
Here,
          P = Principal
          R = rate percent per annum
          T = time for which money is lent/borrowed

Formulas 

1. 1.  Simple interest formula :
        Simple Interest (SI) = \frac { P\times R\times T }{ 100 } 
      
      
   2.  For finding Principal:
          Principal (P) = \frac { 100\times SI }{ R\times T } 
      
      
   3. Calculating Rate percent:
                    Rate% = \frac { 100\times SI }{ P\times T } 
      
      
   4. Calculating Time:
                  Time = \frac { 100\times SI }{ P\times R } 
      
      
   5. To find SI for distinct rate of interest for different periods.
      Suppose,
      ⇒The rate for
      1st { t }_{ 1 } years = { R }_{ 1 } %
      ⇒and rate for
      2nd { t }_{ 2 } years = { R }_{ 2 } %
      ⇒also the rate
      for 3rd { t }_{ 3 } years = { R }_{ 3 } %
      

      The total SI for ({ t }_{ 1 }+{ t }_{ 2 }+{ t }_{ 3 }) years = \frac { P(R_{ 1 }{ t }_{ 1 }+{ R }_{ 2 }{ t }_{ 2 }+{ R }_{ 3 }{ t }_{ 3 }) }{ 100 } 

   6. When the interest is paid “Half-yearly“
       The rate of interest gets half.  
      i.e R ⇒ \frac { R }{ 2 }
      And time will be twice.
       t ⇒2t 
   7. When interest is paid “Quarterly”
      then,
       Rate gets one-fourth
      
      R⇒ \frac { R }{ 4 } 
      And  time will be four times
      t⇒ 4t 
      
      
   8. When a sum of money becomes “x” times in “t” years, then the rate of interest is given by
             Rate= \frac { 100(x-1) }{ t } %
      
      
   9. The difference between SI for a certain { P }_{ 1 } for time { T }_{ 1 } and rate { R }_{ 1 } and another sum { P }_{ 2 } for time { T }_{ 2 } and rate { R }_{ 2 } is given by:
      difference of the SI =\frac { { P }_{ 2 }{ R }_{ 2 }{ T }_{ 2 }-{ P }_{ 1 }{ R }_{ 1 }{ T }_{ 1 } }{ 100 }

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Questions based on Simple interest formulas

If the time is given in month and days