Aptitude - Compound Interest - Discussion

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"Life is like riding a bicycle. To keep your balance you must keep moving."

- Albert Einstein

What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?

[A].	Rs. 2.04	[B].	Rs. 3.06
[C].	Rs. 4.80	[D].	Rs. 8.30

Answer: Option D

Explanation:

C.I. when interest
compounded yearly

= Rs. 5000 x 1 + 4 x 1 + x 4

100 100

= Rs. 5000 x 26 x 51

25 50

= Rs. 5304.

C.I. when interest is
compounded half-yearly

= Rs. 5000 x 1 + 2 3

100

= Rs. 5000 x 51 x 51 x 51

50 50 50

= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04

Ravi said: (Fri, Aug 13, 2010 03:37:30 PM)

Why do we take 2 r in the half-yearly?

Anjali said: (Thu, Oct 14, 2010 07:36:43 AM)

Hello, Since Compound Interest (C.I.) = p[1+{(r/2)/(100)}]^2n for half yearly Thus, C.I.= 5000[1+{(4/2)/(100)}]^{2*(3/2)} =5000[1+{2/100}]^(3) =5306.04

Manisha said: (Fri, Nov 12, 2010 08:54:40 AM)

How we got 3/2 for half yearly for one and half year. please assist.

Binnu said: (Tue, Jan 11, 2011 04:10:56 AM)

According to the question no. of years=1 1/2 so it is equal to 3/2 just(2*1+1)/2

Sachin said: (Wed, Feb 9, 2011 05:33:54 PM)

As per formula it should be, C.I. when interest = 5304-5000 = 304 compounded yearly C.I. when interest is = 5306.04-5000 = 306.04 compounded half-yearly Difference = Rs. (306.04 - 304) = Rs. 2.04

Manikanta said: (Wed, Sep 28, 2011 03:45:32 PM)

What about the Compound interest per year? Why do we take [ 1/2 * 4 ] ?