Aptitude - Compound Interest - Discussion

3. 

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

[A]. Rs. 2160
[B]. Rs. 3120
[C]. Rs. 3972
[D]. Rs. 6240
[E]. None of these

Answer: Option C

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R = 100 x 60 = 10% p.a.
100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.
= Rs. 12000 x 1 + 10 3 - 1
100
= Rs. 12000 x 331
1000
= 3972.


Subash said: (Jul 22, 2010)  
Please explain the use of -1 in C.I calculation. I think here we have to subtract the principle at the back. But u use the value '1' here, I can't understand Wat u r did.

But i got the same answer by using the formula.

C.I = (Amount - Principle)

Where
Amount = {P x (1 + (R/100)^N)} - P
P = 12000.

Therefore, C.I = Rs. (12000*(1+(10/100)^3))-12000 = 3972

Javeed said: (Jul 28, 2010)  
Dude here principle is Rs. 12000, so amount = P(1+r/100)^t

C.I = amount - principle i.e., p((1+r/100)^t )-p

Removing 'p' common factor we get:

p((1+(R/100)^T)-1)

HERE 1200 IS REMOVED AS COMMON FACTOR SINCE IT IS THE VALUE OF P.

Priya said: (Jul 31, 2010)  
Thanks Jeeva. Now I also clear abut this problem.

Anurag said: (Oct 18, 2010)  
Thanks a lot. Now it became very easy.

Kusum said: (Feb 12, 2011)  
Any one tel me how we got R value as 10?

Amit said: (Apr 18, 2011)  
@Kusum

Simple interest formula

SI = PRN / 100

So, SI * 100 = PRN which derives new formula for R as
R = (SI * 100) / PN


Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
Put all this into simple interest formula

R = (100 x 60 ) / 100 x 6 = 10% p.a.

Hope you will get it :)

Karthi said: (Aug 3, 2011)  
How we get P = Rs.100 and S.I = Rs. 60 ?

Arush said: (Sep 15, 2011)  
Thanks jeeva & subash.

Vasanth said: (Oct 5, 2011)  
Why we should take p value as 100?

Anmol said: (Oct 21, 2011)  
@Karthi & Vasanth: you can take any value of P instead of 100.
100 is taken just for simplicity of calculation.
Now, as there is 60% rise in principal in 6 years
therefore, Net amount after 6 years, A= P+ 60% of P =1.6P
therefore interest,I= 1.6P-P= .6P
using SI formula, I= PTR/100
so, 0.6P= P*6*R/100
-> 60=6R
-> R=10%

Shalini said: (Nov 28, 2011)  
I'm totally confused with these problems.

When compound interest is done by individual formulas the answer shows wrong.

Poorvajain said: (Jan 2, 2012)  
CI=AMT-PRINCIPLE

So in this question princple is 100 and u hve taken principle 1 why so is it wrong.

Yamini said: (Mar 4, 2012)  
@Subash

There was no confusion in the given answer, here -1 is nothing but as you said Amount = {P x (1 + (R/100)^N)} - P so from this just take common as P then you get

Amount=[P x {(1 + (R/100)^N)-1}].

Dibyajyoti Hazarika said: (Mar 6, 2012)  
I'm confused about 331 no. How it comes?

Neha said: (Apr 11, 2012)  
@dibyajyoti Hazarika.

(1+ 10/100)^3 -1
After L.C.M. it will be
{(100+10)/100}^3 -1
(110/100)^3 -1
(11/10)^3 -1 //(11x11x11=1331)and (10x10x10=1000)
(1331/1000)-1
After L.C.M.
(1331-1000)/1000
331/1000

I think now you understand about 331

Sunita Sisodiya said: (May 23, 2012)  
Can you help with shortcut method for the same.

Sandip said: (Mar 24, 2013)  
C.I = Rs. (12000*(1+(10/100)^3))-12000 = 3972.

Deepthi said: (May 2, 2013)  
How we get S.I=Rs.60 while P=Rs.100 ?

Vicky said: (May 9, 2013)  
Formula for C.I,

Amount = p(1+R/100)^N, Where amount = Principal + C.I.

Principal + C.I = p(1+R/100)^N.

C.I = p(1+R/100)^N - Principal, ' p ' is a common factor.

C.I = p [(1+R/100)^N-1].

Rajata said: (Oct 9, 2013)  
Its totally wrong hear as compound interest 1200(1+r/1000)n.

As the given formula it should be 12000*1331/1000.

So the answer is..15972.

Steve said: (Dec 4, 2013)  
You make your calculation too complicated for beginners, it would have been much more easier if you just convert it to decimal and ignore the fraction thing. Good job though.

Aayushi said: (Jan 21, 2014)  
Can anyone help me that why do we have to subtract the P. And when to subtract and when not to?

Sarojkumarnaik786@Gmail.Com said: (Apr 26, 2014)  
Generally we know the formula of amount not C.I.

Amount = P(1+ R\100)^t.

If we find C.I then we should subtract the principal, then the formula changes to C.I = P((1 + R/100)^t -- 1).

Bhoomika said: (May 25, 2014)  
What is -1 ?

Nivedita said: (Jun 17, 2014)  
How you have taken P as 100 ?

Satya said: (Jul 24, 2014)  
60% is equal to 60/100 i.e., S.I means adding same rate of interest every year, So here we knew that 60% is increased in 6 years, i.e., Every year it is increased by 10%.

So that 10% * 6 years= 60% for 6 years. So that rate of interest = 10%.

Satya said: (Jul 24, 2014)  
@Nivedita.

Don't bother about 'P'. Think logically about r% using given data.

Josephlecocq said: (Oct 29, 2014)  
Is -1 the same as p?

Angita said: (Nov 8, 2014)  
How SI was 60?

Sandeep said: (Dec 28, 2014)  
Please explain How (1+10/100)^3 is calculated?

Aparna said: (Jul 3, 2015)  
How could it come 331/1000? Shall anyone explain me please?

Hari said: (Jul 12, 2015)  
How to find p=100?

Rohani said: (Jul 27, 2015)  
Why we take S.I as 60 and what is the difference between S.I and C.I?

Aditya said: (Sep 9, 2015)  
S.I is interest on Principle.

C.I is interest of interest.

Beaulah Abigail said: (Sep 27, 2015)  
How the formula C.I = Amount-P comes?

Rahul said: (Oct 21, 2015)  
Brother the answer should be 3852 and a simpler method could be 10 percent of 12000 = 1200 + 10% of 12000 + 10% of 1200 = 1200 + 120 and so on the last will be 1200 + 120 + 12 so grand total 3852.

Prasad said: (Oct 26, 2015)  
Sir question says there is an increase of 60% in amount. How can you take 60 as SI?

Pavan said: (Nov 2, 2015)  
I am getting confusion on this problem can anyone tell me in easy way.

Lee Chong Wei said: (Nov 28, 2015)  
Hi can anyone explain me why CI = Amount-P if its P we can substitute the actual principal.

Dearlie Beloved said: (Dec 30, 2015)  
'I' means increase, since I=F-P. Taking 60 as SI while letting P=100 in i=I/Pn assumes that the future amount will be 60 greater than 100.

We can let P as any number, say P=210, but we need to change I=150 to signal 60 in increase of future amount. We only put P=100 to give justice to the percent sign after 60.

And compound interest is what was asked and not CI rate? Hope this helped.

Vani said: (Jan 23, 2016)  
Suppose principle is 100.

Then simple interest becomes 60.

Then rate will become 10% by using the formula,

(ptr)/100 = simple interest.

Now the compound interest in 3 years with the rate 10% is,

10+10+1(interest on interest)+11+1.1 = 33.1.

12000 --- 100
?----------- 33.1

The answer is 3972.

Durga said: (Jun 6, 2016)  
@ All, Guys your discussions are very useful. Thank you all.

Thejus said: (Jul 29, 2016)  
@Josephlecocq.

What is -1 as p?

Vikash said: (Jul 31, 2016)  
After taking common factor p from bracket then automatically -1 come i.e. -1 * p = -p.

If you are confused about -1 then don't take common answer come same but it becomes some complicated.

Prabhakaran said: (Aug 3, 2016)  
Hi, can anyone explain to me why CI = Amount - P if its P we can substitute the actual principal.

Malleswar said: (Aug 5, 2016)  
Beautifully explained. Thanks to all.

Arvindsamy said: (Aug 11, 2016)  
Guys your discussions and solutions are very useful. Thank you all guys.

Blessing said: (Aug 16, 2016)  
The formula for compound interest:.

A = P (1 + r) ^n.

Now, P = 12000.

A = ?
N = 3.

From the first statement, there was 60% increase in an amount for 6 years simple interest.
Let the amount (P) be 100 then SI=60, SI = PIN.

60 = 100 * I * 6,
60 = 600 I,

I = 0.1.

Since we have 0.1 x 100 = 10%.
Now A = 12000 (1 + 1/10)^3

= 12000 (11/10)^3,
= 12000 (11/10 x 11/10 x 11/10),
= 12000 (1331/1000) = 15,972.
So, A = 15972, P = 12000 then,

CI = 15972 - 12000 = 3972.

Renu said: (Nov 13, 2016)  
10% successive of 3 years is 33.1%

33.1% of 12000.
= 3972.

Angad said: (Jan 5, 2017)  
How to find the rate of interest if compound interest and principle and time is already given but the rate is missing? I need the solution.

Malinimadhavan said: (Feb 5, 2017)  
@Angad.

Formula to find the rate of interest from ci is r= n[(A/P)^1/nt -1].
Now take p=12000; amount (A) = C.I + PRINCIPLE (3972+12000) = 15972; time(t) = 3years n=1.
By substituting this values in the above equation.
r = 1[(15972/12000)^1/3 -1],
= [(1.331)^1/3 -1],
r = [1.1-1],
r = 0.1.

To calculate rate of interest in percentage we use R = r*100.
Therefore R = 0.1*100 = 10%.
Thus rate of interest is 10% p.a.

I hope it will help you.

Victor said: (Feb 7, 2017)  
Please help me to solve this question.

Formula:

Fp=Pp(1+r) raise to power n.
if Pp=100, r=3%,n = 10.

Sammy said: (Feb 23, 2017)  
Thank you so much for explaining the solution.

Sanjay said: (Apr 14, 2017)  
60% is equal to 60/100 i.e., S.I means adding the same rate of interest every year, So here we knew that 60% is increased in 6 years, i.e., Every year it is increased by 10%.

Then, caculate net % for 3yrs.
i.e.
Calculte 1st (10%)and 2nd yr(10%).then result with 3rd yr(10%).

i.e 10+10+(10 * 10)/100 = 21.
Next 21+10+(21 * 10)/100 = 33.1%.

So now just calculate 33.1%12000.
i.e 3972.

Sudarsan said: (Jun 17, 2017)  
Thanks @Neha.

Manisha said: (Jun 25, 2017)  
Thanks @Sanjay.

Dron said: (Jul 27, 2017)  
How to find p=100?

Saleem said: (Oct 19, 2017)  
60%increase in 6 yrs.
i. e 10%every yr.
i. e R=10%.
Now A=P(1+10/100)^3=1200(1+1/10)^3=15972.

CI=15972-12000=3972.

Riya said: (Oct 31, 2017)  
helpful

Mohammad Gazali said: (Nov 19, 2017)  
Please tell me how R=100*60/100*6?

Lokesh said: (Nov 20, 2017)  
How Will find P & S.I?

Moni Shankar said: (Dec 10, 2017)  
1200*(11/10)*(11/10)*(11/10)=15972.
CI=15972-12000=3972,
P.S : (HERE 11/10=110/100 WHICH MEANS 10% RATE AND CAME FROM STATEMENT 60% INCREMENT IN 6 YEARS.)

Aashi said: (Jul 9, 2018)  
Please tell me how 331 is coming? Please explain me.

Rajeev Rathor said: (Aug 26, 2018)  
Using pascal traingle.

= 3*10%of12000+3*10%of1200+1*10%of120,
= 3600+360+12,
= 3972.

Shub said: (Oct 20, 2018)  
Amount after 1st year =1200.
After 2nd year=1200 + 120.
After 3rd year= 1200 + 120+120+12.
Total = 3972.

Bhushan said: (Dec 1, 2018)  
SI for 6 yrs increase by 60%.

Means;
For 1st yr 10%.
1st yr , 10% of 12000 = 1200 - - - >(1)
Add 1200 ... ie. = 12000+1200= 13200.

For 2nd yr, 10% of 13200 = 1320 - - - > (2)
So, 13200+1320= 14520.

For 3rd yr, 10% of 14520 = 1452. - - - > (3)
So add the interest amount of all 3 equations ie....
1200 + 1320 + 1452 = 3972 is the right answer.

Ganesh said: (Dec 5, 2018)  
@All.

1st find rate R of 6 yr Assume 100rs, for 6 yr.
R=(100 * s.i/p * n) = 10%.
After that find C.I using ratio proposition of 3 yr is 3:3:1 is fixed and 2yr is (2:1).
Then 1st yr c.i. is 3* 10% of 12000,
2nd yr C.I is 3* 10% of 1200,
3rd yr C.I is 1* 10% of 120 add all the yrs.
3600 + 360 + 12 = 3972 is the answer.

Sangavi said: (Dec 9, 2018)  
When will we use -P in the compound interest formula?

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