Aptitude - Simple Interest - Discussion
Discussion Forum : Simple Interest - General Questions (Q.No. 7)
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:
Answer: Option
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%
Discussion:
118 comments Page 2 of 12.
Priya said:
1 decade ago
How did they got 105?
Himika said:
1 decade ago
Hows it possible to solve without time?
(1)
Sushmita said:
1 decade ago
SI for 1 year =10.25
10.25=100*R*1/100
=10.25
Hence r=10.25
10.25=100*R*1/100
=10.25
Hence r=10.25
(1)
Sushmita said:
1 decade ago
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 //
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:
1 decade ago
Rate of interest in already given as 10%. Then what is effective rate of interest.
Lakshmy said:
1 decade ago
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//
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:
1 decade ago
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.
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:
1 decade ago
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.
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:
1 decade ago
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.
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:
1 decade ago
In problem he mention that after 6 months the interest is added to sum to calculate principal. So answer is 10.25.
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