Compound Interest (Short-cut method)

Short-cut method:-
    In this method of calculating compound interest we have a formula which was derived in hope of making quicker calculations.

  Advantages of this method:-

1) It makes calculations quicker.
2) It is used in modern days.

  Disadvantages of this method:-

1) It is tougher when compared to Long Method.
2) It is very confusing and takes a long time to get digested.

How it is done?  

Formula:-

                                  

1) Amount = Principal( 1 + Rate )ⁿ

                                                                                          100

n is time period 

2) C.I = P[(1 +  R  )ⁿ  - 1]

                         100

Example Problems:- 

1)  Calculate the Amount & Interest on Rs.40000 at rate 5% for 3 years.

A) P = Rs. 40000

     R = 5%

     T = 3 years

   A = 40000 (1 +  5   ) ³

                           100

      = 40000 (  100 + 5  ) ³

                             100

      = 40000 ( 105 ) ( 105 ) ( 105 ) 

                       100     100      100

      = Rs. 46305

I = 46305 - 40000 = Rs. 6305

Note :- Its all about substituting right values is right formulas. 

 ALL DOUBTS IN THE COMMENTS AND WITHIN 48 HOURS YOU WILL RECEIVE CLARIFICATION.  

Compound Interest (Long Method).

Long Method:-

    In this method the Compound Interest is calculated year by year. The interest for the first year is calculated, added to principal and we get the amount for first year. The amount obtained is then used as principal for second year and amount obtained in second year is used as principal for third year and so on.

   Advantages of this method:-

1) It is non confusing and is easy to use.

2) It provides the student with neatness, since you may not scribble     while using this method.

    Disadvantages of this method:-

1) It is very time taking method.

2) It is an old method and not preferred in modern days.

    

How it is done?

Formula:- If you remember the formula used in calculating Simple Interest this method is waiting for you, but if you don't here it is:-

Formula to calculate interest:-

Interest = Principal x Rate x Time(1 year can be neglected) 

                                          100

Principal = Interest x 100        (Time can be neglected)

                        Rate

Rate = Interest x 100      (Time can be neglected)

               Principal

      Example Problems:-

1) Calculate the amount and compound interest for Rs. 40,000 at an rate of 5% per year for 3 years.

A) Principal (P) = Rs.40000

            Rate (R) = 5%

            Time (T) = 3 years

Interest (I) for the first year:-

        I = P x R x T 

                           100

        I = 40000 x 5 x 1

                  100

        I = 2000 x 1 = Rs.2000

   Amount (A) = P + I

                       = 40000 + 2000

                       = Rs. 42000

I for second year :-

        P = Rs. 42000

         I = 42000 x 5 

                  100

         I = Rs. 2100

    A = 42000 + 2100

        = Rs. 44100

I for third year :-

         P = Rs.44100

         I = 44100 x 5 

                   100

         I = Rs. 2205

    A = 44100 + 2205

        = Rs. 46305

Amount at the end of three years is Rs. 46305 

Interest at end of three years is Rs. 6305 (A at end of 3 years - P)

In calculating P or R we use use their respective formulas. 

Note :- Its all about substituting right values is right formulas. 


 ALL DOUBTS IN THE COMMENTS AND WITHIN 48 HOURS YOU WILL RECEIVE CLARIFICATION.