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.