Aptitude - Compound Interest - Discussion

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

2. 

What will be the compound interest earned on an amount of Rs. 5000 in 2 years?

I. 

The simple interest on the same amount at the same rate of interest in 5 years is Rs. 2000.

II. 

The compound interest and the simple interest earned in one year is the same.

 III. 

The amount becomed more than double on compound interest in 10 years.

[A]. I only
[B]. I and II only
[C]. II and III only
[D]. I and III only
[E]. None of these

Answer: Option A

Explanation:

P = Rs. 5000 & T = 2 years.

I. S.I. on Rs. 5000 in 5 years is Rs. 2000.

   5000 x R x 5 = 2000         R = 8.
100

Thus I only gives the answer.

Correct answer is (A).


Arunkumar said: (Feb 21, 2011)  
Very uesful good keep it up.

Sai said: (Jul 18, 2014)  
If we use PTR/100 formula, P=5000 T= 5 then it will be equal to 250 right? What is that 2000?

Gajendra Bisht said: (Oct 8, 2014)  
In the second option, The compound interest and the simple interest earned in one year is the same.

Since compound interest and simple interest of first one year is same so why this option is also not true.

Pooja said: (Jan 19, 2015)  
I think answer should be E as no option is given that states I and II individually are sufficient.

Raushan said: (Aug 8, 2015)  
Why not answer is (B)?

From first statement it is not clear that amount is being compounded yearly. So for this information, we will need statement (2).

So both 1 and 2 are needed for solution.

Ali Abdullah said: (Aug 14, 2015)  
Data given for compound interest: Present value (P) = 5000 time (t1) = 2-years rate (r) =?

Data given for simple interest: Interest (I) = 2000 time (t2) = 5-years.

Solution:

I = prt.

2000 = 5000(r)(5).

R = 0.08 = 8%.

Rate (r) = 8%.

Compound interest for 1st year: I = s-p.

S = p(1+r/m)^mt.
S = 5000(1+{0.08/1})^(1*1) = 5400.
I = 5400-5000 = 400.

Compounded interest for 1st year.

I (compound) = 400.

Simple interest for 1st year:

I = prt.
I = 5000*0.08*1 = 400.
I(simple) = 400.

So I(simple) = i(compound).

400 = 400.

So (option A and B only) is correct.

In second option I says interest is same for the 1st year and the rate that we calculated was compounded yearly, and was not mentioned whether it was quarterly, semiannually or monthly etc. So if we calculate the interest for the 1st year it is same. As mentioned above.

Prateek said: (Aug 21, 2015)  
For the compound interest, its not mentioned that the sum will be compounded either annually, half yearly or quarterly.

Line I gives the rate of interest and Line II gives the details of sum being compounded at what rate. So answer should be I & II.

Sangeeta Kumari said: (Feb 27, 2016)  
Answer:

It's nothing like annually or quarterly is not being given.

Answer as option A is correct.

Reason:

Option A gives R.

In option B 'R' on both sides get cancelled because when it's given S.I = C.I for one year both become same. So you don't get are as it is cancelled on both R.H.S and on L.H.S.

EXPLANATION:

5000 (1+R/100)^1-5000 = 5000*R*1/100.

5000 ((100+R))/100-5000 = 50R.

50R = 50R.

So from where you would get R! it is cancelled.

And even if we had got are from option B which in this case we are not getting, option should have been I OR II, not I AND II.

Vaibhav Khandelwal said: (May 30, 2017)  
We can use the second statement as well to find the value of R.

Satyam said: (Jun 13, 2017)  
Actually in (A) same principle been used i.e 5000(given).

As well as rate of interest are also same
So p=5000, r=?, t=5.
SI=prt/100.
2000=5000*r*5/100.
r = 2000*100/5000*5.
r = >8.

So, the rate of interest is same as given.

Gaurav said: (Dec 8, 2019)  
What about third option?

Karthik Nl said: (Apr 17, 2020)  
I think the answer should be [D].

I and III only.

In III as well you'll get an equation with only are as variable. P and T is already given, R can be determined from the equation :

10, 000> 5000[1 + (R/10) ]^10.

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