What is a Simple Interest?

                                                   

If we take a loan from a bank. The money you borrow is known as sum borrowed 

or principal. This money would be used by the borrower for some time before it 

is returned. For keeping this money for some time the borrower has to pay some 

extra money to the bank. This is known as Interest. You can find the amount you 

have to pay at the end of the year by adding the sum borrowed and the interest. 

                                  That is, Amount = Principal + Interest

Interest is generally given in per cent for a period of one year. It is written as say 

10% per year or per annum or in short as 10% p.a. (per annum). 10% p.a. means 

on every ` 100 borrowed, ` 10 is the interest you have to pay for one year. 

If the amount is borrowed for more than one year the interest is calculated for the 

period the money is kept for. For example, if  we returns the money at the end of 

two years and the rate of interest is the same then we would have to pay twice the 

interest.

         i.e., ` 800  for the first year and ` 800 for the second. This way of calculating 

interest where principal is not changed is known as simple interest.

 As the number of years increase the interest also increases. For example 100 

borrowed for 5 years at 15%, the interest to be paid at the end of  5 years is 15 + 

15 + 15 +15 +15= 5 × 15 =  75.so,

What is simple Interest?

              Simple Interest (S.I) is the method of calculating the interest where the 

principle  amount of money is same. This concept is used in banks, automobiles, 

finance and so on.

            If we  borrow money from banks in the form of a loan . During payback, 

apart from the loan amount, you pay some more money that depends on the loan 

amount as well as the time for which you borrow. Or if we deposit some amount of 

money after some years we will get some extra money apart from what 

we deposited without changing the principal amount .This is called simple interest.

 

The formula for simple interest 

   simple interest formula helps you to find the  interest amount . Simple interest is given by

             S.I = PRT     

               where P = principal

                          R = rate of interest

                           T = time in years
     

 To calculate the total amount ,we use the formula as              

             AMOUNT = PRINCIPAL + INTEREST

    It can also be written as

                           

     where A = total amount after a given period of time

               R = rate of interest.

               T = time period (in years).

 Benefits of simple interest in real life than compound Interest                   

Simple interest is what it costs to borrow money without compound interest, which

 is interest on the principal and on the interest.

Simple interest is calculated by looking at the principal amount borrowed, the rate 

of interest, and the time period it will cover.

Simple interest is more advantageous for borrowers than compound interest, as 

 it keeps overall interest payments lower.

Car loans, amortized monthly, and retailer installment loans, also calculated 

monthly, are examples of simple interest; as the loan balance dips with each  

monthly payment, so does the interest.

                         

 

What Is the Difference Between Simple Interest and Compound Interest?

Simple interest is the interest based on the principal amount of the loan and 

nothing else, regardless of how long the loan term is. Compounded interest is the 

interest based on the principal amount plus any interest accumulation over time.

                                          

Loans and deposit accounts may use simple or compound interest to determine 

how interest accumulates. When an account uses simple interest, the interest rate 

only applies to the principal balance. But compound interest gets applied to the 

principal balance and accumulated interest.

Over time, an account that uses compound interest can lead to paying (or earning) 

more interest than one that uses simple interest. However, interest is only one 

factor when opening a new account. You may also want to review the accounts’ 

other features, terms, and fees to determine which is best.

Some problems of simple interest using S.I formula

 

Example

Anjali borrow Rs. 19000 at 6 % for 2 years. At the end of 2 years, she  pays Rs. 15000 and a gold ring to the money lender. What is the value of the gold ring? 

Solution

 Principal =19000

           

 Rate = 6%

                  

 Year, T = 2

  Simple Interest, I  = PRT /100

                        

                              = 19000 * 6* 2

               

                              = 228000/ 100

                     

                              = 2280

       Amount,  A = principal + Interest

                            

                         = 19000 + 2280

                           

                         = 21280

    Anjali has to pay amount of 21280 but she only pays 15000 and a gold ring

     

     So the price of the gold ring will be

                                              

                                             = 21280 - 15000

                                              

                                              =6280

Example

Michael pays Rs 9000 as an amount on the sum of Rs 7000 that he had 

borrowed for 2 years. Find the rate of interest.

Solution:

   Amount , A= Rs 9000

   Principal ,P = Rs 7000

   Simple Interest = Amount – Principal

                           = 9000 – 7000 

                           = Rs 2000

   Time = 2 years

   Rate = ?

    SI = (P × R ×T) / 100 

    R = (SI  × 100) /(P× T)

    R = (2000  × 100 /7000 × 2) 

        =14.29 % 

   Thus,  R  = 14.29%   

 Example

Sanjeev borrows Rs 25000 at 8%  per annum for 3 years. At the end  of 3 years, he pays Rs 19000 and a video camera. What is the value of the video camera?

Solution

   P= 25000

    

   R= 8%

   

   T = 3

             

   S.I = PRT/100

   

   I = ( 25000×8×3) ÷ 100

   I = 6000

    A =  P + I

       =25000+ 6000

         

       =31000

       

     After 3 years he pay 19000+ video camera

           

      Value of the camera = 31000- 19000

                                          =12000

Example

 How much time will it take for an amount of Rs. 450 to yield Rs. 81 as 

interest at 4.5% per annum of simple interest?

Solution

   S.I = 81

   R = 4.5 %

   P = 450

   T = ( S.I * 100)/ P *R

      =( 81* 100) / 450* 4.5

      = 4 years

Example

Reena took a loan of Rs. 1200 with simple interest for 2  years as the 

rate of interest. If she paid Rs. 432 as interest at the end of the loan period, 

what was the rate of interest?

Solution

    Principal = 1200

    S.I = 432

    T = 2

    R = ?

     R = ( S.I * 100) / P *T

        =  (432* 100) / 1200* 2

        = 18 %

Example

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 % p.a. in 

5 years. What is the sum?

Solution

 S.I = 4016.25

 R = 9

 T = 5 

 Principal , P = (S.I* 100) / T * R

                     =  (4016.25 *100) / 5 *9

                     = 401625 / 45

                     =  8925

RD Sharma solutions of class X polynomials( Excercise. 2.1) [2023- 2024]

                            

                                          CLASS X   POLYNOMIALS [ Excercise 2.1]

What is a compound interest?

                                      

 INTEREST

           The term Interest is the extra money paid by the institutions like banks or 

post offices on money deposited with them. Interest is also paid by the people 

when they burrow money.

 

COMPOUND INTEREST

      If  we observe the bank statements, we generally notice that some interest is 

credited to our account every year. This interest varies with each year for the same 

principal amount. We can see that interest increases for successive years. Hence, 

we can conclude that the interest charged by the bank is not simple interest; this 

interest is known as compound interest .

What is a compound interest?

       Compound interest is the interest calculated on the principal and the interest 

accumulated over the previous period. It is different from simple interest, where 

interest is not added to the principal while calculating the interest during the next 

period. It is usually denoted by C.I.

                                       

     

What is the formula for finding compound Interest?

 Compound Interest = Interest on principal + Interest over existing interest.

 

So compound interest formula is given by:

                 compound Interest, C.I = Amount - Principal

            where  Amount ,A is given by:

                                         

                            

where  , A = Principal amount

      r = rate of interest

                                                     t = time(no. of the years                                      

    

                                                      n = no. of times interest is compounded per year                  

             when we substitute A in C.I, we have:

                    

                      

where , C.I = Compound Interest

  r = rate of interest   

         t = time (no. of years)   

                                                 n =  no. of times interest is compounded per year

p = principal         

      

  Rate Compounded Annually or Half Yearly     

The C.I formula can be expressed for different situations such as the interest rate 

is compounded yearly, half-yearly, quarterly, monthly, daily, etc.     

             if it is compounded annually then then n will be 1 in the given formula

           

            if it is compounded half yearly for 1 1/2 year then n will be  1+1/2 = 3/2  in the given formula.

 Applications of Compound Interest Formula

There are some situations where we could use the formula for calculation of 

amount in CI. Here are a few. 

(i) Increase (or decrease) in population. 

(ii) The growth of a bacteria if the rate of growth is known. 

(iii) The value of an item, if its price increases or decreases in the intermediate years

Some examples for finding  compound Interest