Monday, May 23, 2011

Innovative shortcuts for finding Compound Interest without calculation...


We all know the traditional formula to compute compound interest.
CI = P*(1+R/100)^N - P

This calculation gets very tedious when N>2 (more than 2 years). The method suggested below is a very simple way to get CI/Amount after 'N' years.

You need to recall the old Pascal's Triangle in following way:
Code:
 
Number of Years (N)                     
  -------------------
        1                        1
        2                    1   2   1
        3                  1   3   3   1
        4                1   4   6   4   1
        .              1 .... .... ... ...   1



Example: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1: 10% of 1000 = 100, Again 10% of 100 = 10 and 10% of 10 = 1
We did this three times becoz N=3.

Step 2:
Now Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331/-
The co-efficients - 1,3,3,1 are lifted from the pascal's triangle above.

Step 3:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331/- (leaving out first term in step 2)

If N =2, we would have had, Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs. 1210/-
CI = 2 * 100 + 1* 10 = Rs. 210/-

This method is extendable for any 'N' and it avoids calculations involving higher powers on 'N' altogether!

A variant to this short cut can be applied to find depreciating value of some property. (Example, A property worth 100,000 depreciates by 10% every year, find its value after 'N' years). 

N.B Prefer this method if N>=3. It will always work and it will save your time like anything.

Stay tuned and you will find many short tricks like this.

14 comments:

  1. Hai, This trick was amazing and it helped me a lot... Thanks.

    ReplyDelete
  2. Please correct
    Step 3:
    3*100 + 3*10 + 1*1 = Rs.331/-

    3,3,3 instead of 3,3,1

    ReplyDelete
  3. really a very good methood.... which we studied in class cbsc class 9th but still not able to apply that........

    ReplyDelete
  4. This trick is Amazing! Could you please tell, how to find Rate, Principle or time through this method?

    ReplyDelete
  5. please give one more short cut this type of questions
    if principal is 10000/- rate is 10% calculate CI for 2 year and 4 months

    ReplyDelete
    Replies
    1. for 2 years:
      (10%+10%)+(10%*10%)=21%,
      21%of 10000=2100
      for 4 months
      amount=10,000(1+(10/4)/100)^4*2
      =(approx)11597;
      C.I=A-P;
      1597;
      now 2100+1597=3697

      Delete
  6. Let me know apply this formula for 4 years problem

    ReplyDelete
    Replies
    1. I mean

      P = 1000, R=10 %, and N=4 years. What is CI & Amount?

      Delete
    2. It applies for 4 years and beyond also ..
      For Y=4, co-efficient is 1 4 6 4 1
      10% of 1000 = 100
      10% of 100 = 10
      10% of 10 = 1
      10% of 1 = 0.1

      So Compound Amount = 1000*1 + 100*4 + 10*6 + 1*4 + 0.1*1
      = 1000 + 400 + 60 + 4 + 0.10
      = 1464.10

      Delete
  7. It applies for 4 years and beyond also ..
    For Y=4, co-efficient is 1 4 6 4 1
    10% of 1000 = 100
    10% of 100 = 10
    10% of 10 = 1
    10% of 1 = 0.1

    So Compound Amount = 1000*1 + 100*4 + 10*6 + 1*4 + 0.1*1
    = 1000 + 400 + 60 + 4 + 0.10
    = 1464.10

    ReplyDelete