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).

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

ReplyDeletePlease correct

ReplyDeleteStep 3:

3*100 + 3*10 + 1*1 = Rs.331/-

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

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

ReplyDeleteVery nice.Thank you.

ReplyDeleteNice method.Thanks for helping me out

ReplyDeleteThank you

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

ReplyDeleteplease give one more short cut this type of questions

ReplyDeleteif principal is 10000/- rate is 10% calculate CI for 2 year and 4 months

for 2 years:

Delete(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

Let me know apply this formula for 4 years problem

ReplyDeleteI mean

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

It applies for 4 years and beyond also ..

DeleteFor 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

it can't apply for 4 years.

ReplyDeleteIt applies for 4 years and beyond also ..

ReplyDeleteFor 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