Aptitude - Compound Interest - Discussion

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

So the reason CI is subtracted with P ([CI-P]-si) here is because;

CI calculates the amount after the principal has been compounded, that is it includes the compounded interest to the initial principal.

If the principal was 100 in this problem then CI would've been 108.16 (if I'm not wrong), which would include the interest (8.16) that has been added to the initial principal of 100.

So, yeah the formula for ci is more like 'compounded amount' (ca) rather than compounded interest. To find out exactly how much interest has been compounded you have to subtract 'ca' with the principal amount.

Hi.

Before solving this question you have to be aware on S.I and C.I formula's.

S.I = PTR/100.

Where as AMOUNT = P (1+ R/100) ^T ====> IN C.I.

AMOUNT = P + C.I.

C.I = P (1+ R/100) ^T - P.

In the question, they give the difference between S.I AND C.I is rupee 1.

First Calculate S.I.

Let the PRINCIPAL or SUM be ==> '' P '', TIME = 2, RATE = 4%.

S.I = PTR/100 ==> P*2*4/100 ==> 2P/25.

Now C.I = P (1+R/100) - P ==> P (1+4/100) - P ==> 51P/625.
51P/625 - 2P/25 = 1.
LCM IS 625.
51P - 50P/625 = 1.
P = 625.

I hope this will be helpful.

Thank you.

Take as, C.I - S.I = Rs.1.

Then, for C.I ->use the Formula[x + y + {(xy)/100}].

For x&y ->put R% value( i.e.,) X=4 &y=4.

By this ,we get [4+4+{4*4/100}] = 8.15.
For S.I -> R * T = 4 * 2 = 8.
So , 8.15 - 8 = RS.1 => 0.16=1.

By this, 0.16% = 1 means,then 100%=?
So, cross multiply it
i.e., 100 * 1/0.16 = 625.

I am just trying to explain briefly, hence the sum looks like long . But you all just write the numerical step and look it .
It just takes few secs only try it.

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.

@Tamana.

Hey its simple sum just Few steps,

Step 1:
Compound interest = p(1+R/100)^n - p.
[Here p is subtracted from total amount at end of annum to find out compound interest].

Step 2:
Simple interest= pRn/100.

So,

Compound interest - simple interest = 1 Rs.
p(1+R/100)^n - p - pRn/100 = 1.
p(1+4/100)^2 - p - p*4*2/100 = 1.
p(1.04)^2 - p - p*.08 = 1.
p(1/625) = 1.

So p= 625 Answer.

Explanation:
Let initial amount P = X.
R=4, T=2.
Now,
SI = P * R * T/100 = x * 4 * 2/100 = 2x/25.
SI = 2x/25.
CI = P[1+R/100]^T-x = x[1+4/100]^2-x.
= x[1+1/25]^2-x,
= x[26/25]^2-x,
= x[676/625]-x,
=676x/625-x,
=676x-625x/625,
=51x/625,
CI = 51x/625.

According to the question.
CI-SI = 1.
51x/625 - 2x/25 = 1.
51x-50x/625 = 1.
X = 625
So, P = 625.

It is simply derived by using this formula => Diff =PR^2/100^2 -> It is only for 2 years difference.

Given -> Diff=1 , R =4, Tp find P?

By Formula ,
Diff = PR^2/100^2.
1 = P * 4 * 4/100 * 100.
1= P * 1/20 * 1/20.

Note : (Also for three years difference use this formula -> Diff = PR^2(300 + R)/100^3).

S.I = PNR/100.
=(PX2X4)/100,
=(PX2X1)/25.

THEREFORE S.I = PX2/25 = 0.008P,
C.I = P(1+R/100)^N -P,
= P(1+4/100)^2 -P,
=P(1+1/25)^2 - P,
= P(25+1/25)^2 -P,
= P(26/25)^2-P,
= P(1.04)^2-P,
= P(1.0816)-P,
=1.0816P-P.
C.I =.0816P.

DIFFERENCE:
CI-SI = 1
0.0816P - 0.08P =1,
0.0016P = 1,
P = 1/0.0016 = 625.
THEREFORE, SUM IN RUPEES IS 625Rs.

Suppose that we take the sum 100.

2 years simple interest of 100 is 108.
And 2 years compound interest of 100 is;
108.16.

The difference between two interests is 108.16-108 = 0.16;
Now we can say that;
0.16 difference than 100 sum.

1 difference then what will be the sum?

Hence
0.16 : 100 :: 1 : ?
100×1
--------
0.16
= 10000/16.
= 625.