Simple & Compound Interest

Simple & Compound Interest
     Simple  Interest:-

      Simple interest is a method of calculating the interest charge on a loan( amount).

      Simple interest is calculated on a amount borrowed for entire period at a rate 

      of interested.

   The formula of Simple Interest :-

                 SI = {(P ✕ R✕ T)/ 100}   

Where, P = Principal  (the original loan)

             R = Rate of interest (at which the loan is charged)

             T = Time period (the duration for which money is borrowed)

            Amount = Principal +SI

Compound Interest :-

Compound interest is calculated on the principal amount and also on the accumulated

 interest of previous periods.

The formula of Compound Interest :-

              

  Where, P = Principal  (the original loan)

              R = Rate of interest per year  (at which the loan is charged)

             T = Time period in years (the duration for which money is borrowed)
 The formula of Amount :-

Note:-If  the interest is compound half yearly Rate will be half and time will be doubled.                         i.e. formula to be used 

              If  the interest is compound  quarterly Rate will be one fourth 

              and time will be four times.

              i.e. formula to be used 

          If  rate of  interests are R₁ ,R₂,R₃ for first year second year third year.

Example 1. A sum of Rs. 2500 becomes Rs. 2725 at the end of 3 years 

                    when calculated at simple interest. Find the rate of interest.

Explanation:-Amount = 2725,Principal = 2500

                        Simple interest = 2725 – 2500 = 225

                         Time = 3 years, Rate=R = ?

                         Formula     SI   = {(P ✕ R✕ T)/ 100}   
                                          225  = {(2500✕ R✕ 3)/100}
                                            R   =   (225✕100)/(2500✕3)
                                            R   =     3%
Example 2  A sum of money at simple interest amounts to Rs. 815 in 3 years 
                   and to Rs. 854 in 4 years. What is the sum is.
Explanation:-Amount after 3 years = 815
                        Amount after 4 years = 854,Principal = P = ?

                      S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

                      S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

                      Principal = Rs. (815 - 117) = Rs. 698

                      Hence Principal =  Rs. 698

Example 3.  Ram took a loan of Rs. 1200 with simple interest for as many                                                  years as the rate of interest. If he paid Rs. 432 as interest at the                                                 end  of the loan period, what was the rate of interest.

Explanation:-  P = 1200, SI = 432 Rate = R %,Time = R Years

                          Formula     SI   = {(P ✕ R✕ T)/ 100}   

                                            432 =  {(1200✕ R✕ R)/100}

                                            432 = 12 R²

                                                  R² = 36

                                             R = 6

                      Hence Rate = 6 %,Time = 6 Years

Example 4.  The simple interest on a certain sum of money for 2 and 1/2 years at
                       12% per annum is Rs. 40 less than the simple interest on the same
                       sum for 3 and 1/2 years at 10% per annum. Find the sum

Explanation:-Let the sum =.X   Difference of SI Between (7/2 -5/2) years = 40
                         [{x×10×7}/{100×2}] – [{x×12×5}/{100×2}] = 40
                         {70 x/200 - 60x/200} = 40
                         10x/200 = 40
                           x = 800.
                         Hence Principal =  Rs. 800.
Example 5.  At what rate percent per annum will a sum of money double in
                      8 years.
Explanation:-   Amount = 2P ,P = P, SI = P , Rate = R %,Time = 8 Years
                           SI   = {(P ✕ R✕ T)/ 100}  
                            P = (P ✕R✕ 8)/ 100
                           R = 25/2 = 12.5%
                          Hence Rate = 12.5%
Example 6.  The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. 
                     What is  the period (in years) .

Explanation:-   P = 30000, CI =4347 ,Amount = P+CI= 30000+4347 = 34347,
                           Rate = 7 %,Time =  ?

                                                              T = 2 years
Example 7.  What will be the compound interest on a sum of Rs. 25,000 after 3 years
                      at the rate of 12 % per annum?

Explanation:-   P = 25000, CI =? ,Rate = 12 %,Time = 3 years

Example 8.  What is the compound interests on Rs. 5000 for 1 and 1/2 years
                     at 4% per annum  compounded half-yearly?

Explanation:-   P = 5000, CI =? ,Rate = 4 %,Time = 1 and 1/2 years
                                                       Rate = 2% Time = 3 years

Example 9.  Simple interest on a certain sum of money for 3 years at 8%
                     per annum is half the compound interest on Rs. 4000 for 2 years 
                     at 10% per annum. The sum placed on simple interest is.

Explanation:-  For CI : P = 4000, Rate = 10 %,Time = 2 years

For SI: Rate = 8 %,Time = 3 years,SI = 420,P = ?