Aptitude - Simple Interest - Discussion

7. 

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

[A]. 10%
[B]. 10.25%
[C]. 10.5%
[D]. None of these

Answer: Option B

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs. 100 x 10 x 1 = Rs. 5
100 x 2

S.I. for last 6 months = Rs. 105 x 10 x 1 = Rs. 5.25
100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%


Ankit Saxena said: (Aug 21, 2010)  
Question did not mention that the interest is to be calculated for 1 year only.

Kiran said: (Jun 19, 2011)  
Total Simple Interest is Rs.5.00+5.25 = 10.25
How can we say that it is a rate of interest whereas it is formula of calulating simple int.

Punna said: (Jun 24, 2011)  
Why we take last 6 months principal as 105?

Ravish said: (Jul 6, 2011)  
Because question suggests that "he includes the interest every six months for calculating the principal".

Shweta said: (Aug 19, 2011)  
I did not get, how 10.25 is consider as rate not S.I. ?

Can anybody help me and Kiran ?

Kalam said: (Aug 19, 2011)  
Time should be mentioned here.

Or have to say that at the end of year.

Varun said: (Aug 31, 2011)  
I am not getting that why are they multiplying 2 in the first 6 and in last 6 months ? Can any one provide me with the full and correct explanation for this?

Devi said: (Aug 31, 2011)  
For half of the year we take 1/2 (for 6months) and also by adding another 1/2 for next 6 months we get the total amount for a year.

Varun Mathur said: (Sep 1, 2011)  
How did they got 105 and why are they multiplying it 2?

Please explain me.

Sumit said: (Sep 4, 2011)  
S.I is always calculate on original sum. But here the last six month S.I is calculate on Amount at the end of 1st 6 month. Is'nt this is the concept of C.I not of S.I ?

Priya said: (Sep 7, 2011)  
How did they got 105?

Himika said: (Oct 5, 2011)  
Hows it possible to solve without time?

Sushmita said: (Feb 8, 2012)  
SI for 1 year =10.25
10.25=100*R*1/100
=10.25
Hence r=10.25

Sushmita said: (Feb 8, 2012)  
As amount is not given so we will have to consider the amount to be 100
hence let P=100.

Now the lender add interest after every six month so we will have to calculate SI for every six month add then add this SI toh the P.

Hence
SI=P*R*T/100
=100*10*1/100*2(6 monh=1/2 year)
=5

Now P becomes
P=100+5
=105, this is SI for 1st 6 month
Now calculate SI for last 6 motnh
SI=105*10*1/100*2
=5.25
P=5+5.25+100
=110.25, this is the amount at the end of 1 year.

Now SI for I year=110.25-100
=10.25
Now we have to calculate rate
SI=P*R*T/100
10.25 =100*R*1/100
R=10.25 //

Haritha said: (Mar 24, 2012)  
Rate of interest in already given as 10%. Then what is effective rate of interest.

Lakshmy said: (Aug 6, 2012)  
Say X is the Principal amount
then SI for first the 6 months= X*10/100*1/2 =X/20

SI for the next 6 months =21X/20*10/100*1/2= 21X/400
[Here Principal amount is taken as X+ X/20= 21X/20]

SI for one year =X/20+ 21X/400 = 41X/400

Now With Principal amount X and SI 41X/400 for one year we have to find the rate of interest, say y
y= 100*41X/400*1/X = 10.25//

Shrikanth D said: (May 3, 2013)  
Here is a shortcut for you.

Interest is 10% percent that means per year 10 rs will increase. If you take 100 as principal that means interest would be 5 Rs for 6 months. Now the total principal becomes 105 now again 5% interest for 6 months becomes 5.25. Now total interest is 5+5.25 = 10.25.

Otherwise x+y+(xy/100) = 5+5+(25/100) = 10.25.

Divesh said: (Aug 6, 2013)  
Total amount after 1 year 110.25. Principal is 100 So SI = 10.25.

SI = PxRxT/100.

10.25 = 100 x R x 1/100.

R = 10.25.

In the solution they directly its written as effective rate.

Vignesh said: (Aug 16, 2013)  
It is said as SI. So even for the second half of the year the principal should be taken as 100. Here it is taken as 105 which is in case of CI.

My answer:

For first 6 months :

ASSUME p = 100 AND r = 10%.

SO INTEREST IS 10 RS AND AMOUNT = 110.

FOR NEXT 6 MONTHS :

SAME P = 100 AND R = 10% AND WE WILL GET THE SAME INTEREST WHICH IS 10.

NET INTEREST = 20.

Net amount = 120.

So answer should be 20%. option D.

Answer will be 10.25 if its CI.

Kindly correct me if I am wrong.

Ravi said: (Aug 20, 2013)  
In problem he mention that after 6 months the interest is added to sum to calculate principal. So answer is 10.25.

Megan said: (Aug 21, 2013)  
10% is already given as the interest then what do you mean by effective rate of interest?

Sravani said: (Oct 3, 2013)  
Can any one explain in easy way ?

Raja Ab said: (Oct 24, 2013)  
10 % per year = 10 on 100.

So first we calculate for 6 months so 10/2 = 5 which is S.I 1 .

So 5 is add to supposed amount because in Q mention that, So principal amount 105, so next 6 month we take int 10% on 105. So S.I 2 = 5.25.

Add both int values 5+5.25 = 10.25 I think that is simple.

Shilpa said: (Jan 18, 2014)  
What is effective rate of interest?

Spandana said: (Feb 15, 2014)  
What is effective rate of interest? diff between effective rate and rate?

Rahul said: (Feb 20, 2014)  
If we consider 105 as a principal for next 6 months than it is not S.I it should be C.I.

Janani said: (May 2, 2014)  
How we do without time friends? How you took 1 yr?

Deekshit said: (Jul 15, 2014)  
Is they calculated for SI or CI?

Amit said: (Oct 11, 2014)  
Period has not been mentioned?

Naznin said: (Oct 15, 2014)  
@Amit.

Here given that "Effective rate of interest" which is for period of 1 year..effective rate means rate for one year.

Question said: (Jan 22, 2015)  
If the lender increase interest in every 24 months or 2 years then formula is would be ?

Gautam said: (Mar 22, 2015)  
The explanation is incorrect.

Actually it is a CI problem.

Let actual rate be r. Effective rate be R.

And time period be n years. Then SI = CI-P.

P*R*n/100 = P(1+r/200)^2n - P.

P*R*n/100 = P[(1+10/200)^2n - 1].

R = [(1.05)^2n - 1]*100/n.

Now if n = 1 then only are = 10.25.

So, correct answer is (D). None of these.

Divya Agrawal said: (Mar 31, 2015)  
If for one year is x. And if calculating with 6 month, for one year it should be 2x?

Kanav Gupta said: (Jun 19, 2015)  
@Divya Agrwal.

As you said for one year it is x. Then for 6 months it is x/2 and thus again for one year is 6 months + 6 months i.e. x/2+ x/2 = x. I know it is little bit confusing.

Rebelzzz said: (Jul 2, 2015)  
Anybody please clarify me it. Am not able to understand.

In the question it is mentioned that amount is calculated on simple interest. Then why did the take 105. It 105 take, then it should be CI. Help me please.

Manohar said: (Jul 13, 2015)  
The logic in question is "He includes the interest every six months for calculating the principal". By considering it in 1st 6 months he got 5.00 as S.I.

As per the logic, he included the 5 rs S.I with principal amount and it becomes 105. Effective rate is nothing but (total amount-principal amount). (up to my knowledge).

Pramod Kajla said: (Aug 22, 2015)  
Time should be mentioned in the question as 1 year.

Pramod Kajla said: (Aug 22, 2015)  
Time should be mentioned in the question as 1 year.

Rose said: (Aug 25, 2015)  
Please can anyone give a better explanation.

Bhushan said: (Sep 4, 2015)  
Hi, we can solve this problem by using compound interest method. Such as interest compounded half yearly.

R = 5%, P = 100.

A = p{1+R/100}^2.

A = 100{1+5/100}^2.

A = 110.25.

V!Cky said: (Sep 24, 2015)  
a+b+ab/100 net interest you get 10.25.

Si = 5% for 1 year next year will be same.

Anil Kumar said: (Jan 31, 2016)  
Let the sum be Rs. 100. Then, for six month time will be (6/12) year which become 1/2 year.

S.I. for first 6 months = Rs. (100 x 10 x 1)/100*2 = Rs. 5.

Now Principal for next 6 months will 100+5 = 105.

S.I. for next 6 months = Rs. (105 x 10 x 1)100*2 = Rs. 5.25.

Total interest in a year 10.25.

Apply formula:

S.I. = P*r*t/100.

Put value for a year now.

10.25 = 100*r*1/100.

R = 10.25*100/100*1.

R = 10.25%.

Suraj said: (Feb 6, 2016)  
They take the interest of 1\2 year for six month because divided by 100*2 not 100 for simple take T = 1/2.

Sanshunoisky said: (Jun 13, 2016)  
Hey there you all take the si as 105 for the next 6 months but note that it will not be simple interest. That will be a compound interest (ci).

John said: (Jun 13, 2016)  
Why not the value of P be 1000?

Jaya said: (Jul 2, 2016)  
See guys the reason why they added 105 for next six months is.

Read the question carefully they mentioned as ''he INCLUDES THE INTEREST every six months for calculating the principal''. So they added the interest + principal for every 6 months.

Its a trick actually SI is not calculated but they indirectly telling its CI.

Rahul said: (Jul 2, 2016)  
But the answer will be different for different P.

If I take P = 200 instead of 100, then the answer will be 20.5%.

Sandy said: (Jul 6, 2016)  
If I take P = 10 instead of 100, then the answer will be 1.02%?

Why the value of P be 100?

Guys try to help me, I need answer.

Kiran said: (Jul 17, 2016)  
Why p = 100?

Nikita said: (Jul 18, 2016)  
For next 6 month why it takes as 105, in simple interest principal which is always same.

Jatin Lalwani said: (Jul 25, 2016)  
No, its wrong.

For first six months, they are using 100.

For next six months, they are using 100 + (interest of previous six months).

This is the concept of Compound interest, not Simple interest!

Pavan said: (Aug 6, 2016)  
Why are we taking only p = 100?

If we take p = 10 can we get the answer?

Ramesh said: (Sep 18, 2016)  
Why has he taken 10% interest rate instead of taking 6 months interest rate?

Time is taken for 6 months but interest is not taken for 6 months.

Ramesh Yadav said: (Sep 21, 2016)  
@Ramesh

10% means 10 for every 100 only, and 10% p.a means 10 for every 100 per annum but they did not mention 10% p.a in question.

Prashant Singh said: (Oct 22, 2016)  
For those who don't understand why here 2 is multiplied as in a formula, time is mention as a year. So we are taking a month. Then we have to convert into the year by multiplying 1/2.

Guru said: (Oct 23, 2016)  
I think by taking 105 as the principal amount for last six months, they are partially compounding it. So I think the process is not correct.

Sravani said: (Nov 22, 2016)  
If we take 105 as last 6 months principal then it is not simple interest it's like compound interest.

Kapil said: (Jan 29, 2017)  
Why we divide it by 2 for find the simple interest for 6 months?

Seemanchal Das said: (Feb 4, 2017)  
According to Answer:

Let principal is 100
So si= P * R * T/100.

Then we get 5.
Principal for next 6 month is 105.
My question is why 5 is add with principal?

Ammu said: (Feb 28, 2017)  
Here we are calculating simple interest in half yearly basis. Then how it become 10.25?

Patel said: (Mar 20, 2017)  
It was S.I. not a compound interest. then why you have consider the 105rs as a sum of next 6 months?

It should be 100 only.

Konok said: (May 18, 2017)  
We can find effective interest rate by the following formula.

EAR (effective annual rate) = [(1+r/m)^m]-1.
Where r means interest rate.
Here, m means the number of compounding period.
Here our require ans is [(1+.10/2)^2]-1.
= .1025.

where r = 0.10.
m= 2 ( it is 2 because every six months come two time in a year).
= 10.25 %.

Riya Das said: (Jul 8, 2017)  
Why we subtract the final amount from the sum to get effective rate?

Arpit said: (Jul 23, 2017)  
Hi all,

I understood that we got 105 as we have assume 10% as interest for whole year so if we assume principal as Rs. 100 for 6 month @ 5% and then for remaining month we add 5% to Rs. 100 we get Rs. 105, but my question here is that if we follow this concept why we took complete 10% for calculation of 6 months?

Ram said: (Jul 28, 2017)  
The solution has compounded the interest instead of simple interest.

Monica said: (Aug 1, 2017)  
Well said @Sushmitha.

Vaibhav Kadu said: (Aug 7, 2017)  
Here, it is not mentioned to calculate for one year tenure.

Seyedali Fathima said: (Aug 9, 2017)  
How do consider amount p=100?

Maggi said: (Aug 24, 2017)  
6 months is considered 1/2 (Time =1/20).

In the question the person charges for 6 months instead of 1 year.

So effective interest is asked 5% in first 6 and 5.25 in next.

Harika said: (Sep 18, 2017)  
Superb explanation. Thank you all.

Purusottam said: (Sep 29, 2017)  
If we follow the Compound interest formula it will be easy like watery bubbling.
Suppose principal =100
Amount =p(1+r/100*2)^2n
=100(1+10/2*100)^2*1
=110.25.

Now, CI=A-P
=110.25 -100
=10.25%.

Rahul said: (Oct 2, 2017)  
Why we are charging interest on interest this is simple interest, not compound interest?

Gautham said: (Dec 12, 2017)  
Why should we need to consider the amount to be 100?

Ravi Das said: (Feb 9, 2018)  
Let the sum be Rs. 100. Then,

S.I. for first half year = Rs. (100 x 10 x 1)/(100x2) = Rs. 5.
S.I. for last half year = Rs. (105 x 10 x 1)/(100x2) = Rs. 5.25.
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25.
Effective rate = (110.25 - 100) = 10.25%.

Pooja said: (Apr 3, 2018)  
Why the total sum is 100?

Nathan said: (Apr 7, 2018)  
We can as well take the sum(P) to be 200.

After calculating the simple interest in 6months we get 10,
Add that 10 to the sum making now 210 repeat the tabulation for interest for the remaining months 6.

Then, you get 10.5.

Add the two 10+10.5=20.5.
So. total simple interest is 20.5/200 x 100 which is 10.25.

Khushi said: (Apr 13, 2018)  
Thank you @Sushmita.

Manish Kumar said: (Apr 27, 2018)  
The rate is always annual(Not necessary to mention).

If it is not mentioned then we have to understand it is 10 p. a.

But in this question interest is calculating at every six months so rate (10/2 =5%).
So, Rate is 5 % for six months,
Now, financier includes interest after 6 months that means He will give interest on the interest that means he will give interest 5% on 5.

So, it is 5*5/100=0.25,
one year interest =5+5+=10%,
But effective interest =10+0.25=10.25,
(here 0.25% is interest on interest)

Doesn't matter if you are taking p=100 or p=200 or p=10.
But interest is always on 100.

If it is given 5% then it means we got an interest of rupees 5 on rupees 100.

If you are taking p=200 and rate is unchanged (5%) then we got 10 rupees interest on 200.
In this case, we are also getting 5 rupees on every 100 rupees.
So in this question, you take principle 100 /200/10 but we get effective interest =10.25.

Raghu said: (Apr 28, 2018)  
For six months 100*1/2=50 but they have taken 100*2 why?

Priya said: (Apr 30, 2018)  
Thank you @Sushmitha.

Aditya said: (May 7, 2018)  
100*r*1/100=10.25 since p*r*t/100= S.I
By, solving we will get r = 10.25 answer.

Arun said: (Jun 13, 2018)  
Why they are assuming p as 100 why can't we take any oter values?

Vikul Chauhan said: (Aug 22, 2018)  
The easiest way to do this question is;

Let principal =100.
A=100 [1+4/100] =112.4864.
The interest of one year 12.48.
Effective rate of interest = 12.5%.

Akash said: (Aug 26, 2018)  
Please tell me, why calculating compound interest for the second half, (since compound interest is interest on interest).

I think the formula should be pr (2T)/100 because we take interest twice a year.

Bijata said: (Nov 24, 2018)  
The effective rate of interest = [1+I/2]^2 -1,
= [1+0.10/2]^2-1,
= [1.05]^2-1,
= 1.1025 - 1,
= 0.1025*100.
= 10.25%.
Note: ^2= it is said for only six month.

Kalpesh Sahu said: (Feb 25, 2019)  
eff. interest = ( (1 + r%/(100*t) ) ^ t - 1 )* 100.
r% = rate of interest (10).
t = time divided (in this case = 2).

Soln; ( (1 + 10/(100*2) ) ^ 2 - 1 )* 100,
= ( (1 + 10/200 ) ^ 2 - 1 )* 100,
= ( (1 + 0.05 ) ^ 2 - 1 )* 100,
= ( (1.05)^2 - 1 )*100.
= ( 1.1025 - 1 )*100.
= ( 0.1025)*100,
= 10.25%.

Jhansi said: (May 31, 2019)  
@Kalpesh.

What is eff.interest?

Rk Hasan said: (Sep 29, 2019)  
it is compound interest actually,

Amount(A) = P(1+10/(2*100))^(2*1) = P(1.1025).
Interest = nr = r = A-P = 0.1025 = 10.25%.

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