Wednesday, January 6, 2010

Compound Interest Shortcut

A good shortcuts on Compound Interest.
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We all know the traditional formula to compute interest...
CI = P*(1+R/100)^N - P
The calculation get very tedious when N>2 (more than 2 years). The method suggested below is elegant way to get CI/Amount after 'N' years. You need to recall the good ol' Pascal's Triange 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 b'cos N=3.
Step 2:
Now Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331/-
The coefficents - 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).

10 comments:

  1. This method is really simple. Thank you. Can you post such methods for calculating CI if the N is quarterly, half yearly and in any number of months. Your help would be appreciated.

    ReplyDelete
    Replies
    1. Consider half yearly

      In this case the rate will be half of annual rate calculated halfyearly

      i.e Rate = 5% and N=6 for the above case

      Similarly do the necessary for quaterly

      Delete
  2. if you want half yearly and quarterly then for

    half yearly rate will half and time will double

    similarly for quarterly rate will one forth and time will four time

    ReplyDelete
  3. can we have shortcuts for solving percentage aptitude questions?
    the above one was of great help!!

    ReplyDelete
  4. brother...........I want be a member of ur blog.....can I ??????????

    ReplyDelete
  5. Thank u brother...its really superb..........

    ReplyDelete
  6. amazing....thanku...so much!

    ReplyDelete
  7. Where do we consider Rate 'R' using Pascal's triangle method ?? What if the rate is 5% where should we submit ??

    ReplyDelete
  8. how to find rate of interes if CI,N and p given in shortcut...

    ReplyDelete