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Aptitude - Compound Interest - Discussion

@ : Home > Aptitude > Compound Interest > General Questions - Discussion

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"To err is human; to forgive, divine."
- Alexander Pope
2. 

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

[A]. 625[B]. 630
[C]. 640[D]. 650

Answer: Option B

Explanation:

Let the sum be Rs. x. Then,

C.I. = x 1 + 4 2 - x = 676 x - x = 51 x.
100 625 625

S.I. = x x 4 x 2 = 2x .
100 25

51x - 2x = 1
625 25

x = 625.
Goutham said: (Wed, Jul 14, 2010 12:43:27 AM)    
 
Hai I am Goutham.

Can anyone help me out , why are we using -x in the step one..

Please help me out
Thanks in advance...
Xyz said: (Sun, Jul 18, 2010 12:32:12 PM)    
 
CI = interest- sum............
observe problem 1 . CI= 3321-3200
Gutti said: (Sun, Aug 1, 2010 01:52:17 AM)    
 
You have any shortcut method to this.
Name said: (Fri, Sep 17, 2010 08:11:41 AM)    
 
P x 4/100 x 4/100 = 1

P = 25*25 = 625
Priyanka P. said: (Thu, Dec 2, 2010 07:44:29 AM)    
 
its p*(x/100)^2 = ans.

p=amount
x=rate
Prudhvi said: (Wed, Dec 22, 2010 12:34:56 AM)    
 
Hai I'm prudhvi. Can any one help me out?

Why are we using 676/625x in the step one?

Please help me.
Krishna said: (Fri, Dec 24, 2010 12:07:20 PM)    
 
Hello friends!

The question is very easy . First know the diff b/w S.I. and C.I.

S.I. = P*T*R/100
Amount = S.I. + P

C.I. = Amount - P
Amount = P*((1 +(R/100))^ n) where (n= no of years)

Given that S.I. and C.I diff is 1rupee

and also given T=time =2 yrs , R=rate = 4%,
and he asked P ie Principal Amount.


So S.I. = P*2*4/100; = P*2/25;
C.I. = Amount - P

= P*(1+ (4/100))^2 - P

= P*(1 + (1/25))*2 - P
= P*((26/25)^2) - p
= P*(676/625) - p

= (P*676-P*625)/625
= (P*51)/625

WE KNOW S.I. = (P*2)/25

AND S.I.-C.I. = 1
HENCE
(P*2)/25 - (P*51)/625 = 1
BY SOLVING U GET
P = 625 RS
Vivek said: (Thu, Feb 3, 2011 07:18:20 AM)    
 
How to solve very simple?
Kusum said: (Sat, Feb 12, 2011 10:18:46 AM)    
 
Please any one tel me how to solve it in simple method.
Viji said: (Mon, Jul 4, 2011 06:19:31 AM)    
 
shotcut method:
If you give the difference between si and ci for 2 years means,
4*4/100
=.16
1/.16*100
100/16*100
100/4*25
625
Sudharsan said: (Sun, Sep 18, 2011 10:01:31 PM)    
 
For beginners those are asking why they used -x in step one.

Let me explain you clearly.

First take Amount=Rs.5000 and Rate=2% Years=1

Then calculate SI, SI=PNR/100

So, SI=5000*1*2/100=RS100

[Here you are getting only interest]

Now calculate CI, CI=P(1+r)^n

So, CI=5000*(1+2/100)^1=RS5100

[Here we are getting interest+Principal amount]

That's why there are using -x in the formula.

If you use -x(for our example its P) we will get the interest only.
Vishal Kumar said: (Tue, Sep 27, 2011 09:59:49 AM)    
 
Shortcut method

Difference = (D*R^2)/100^2 for 2 year

Difference = {(D*R^2)(300+R)}/100^3 for 3 year.
Siva said: (Mon, Oct 17, 2011 11:38:30 AM)    
 
@sudharshan.

Rightly said, cleared because of you.
Atanu said: (Sat, Dec 10, 2011 07:49:42 PM)    
 
Shortcut Method

sum = difference*(100/R)^2 for 2 year

sum = {difference*(100^3)}/{R^2*(300+R)} for 3 year
Rajeev said: (Sat, Dec 10, 2011 08:08:55 PM)    
 
A=P( 1+R/100)
C.I=A-P
DIFFERENCE OF CI AND S.I FOR X YEAR= P*(R/100)^X
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