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.
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.
Manohar said:
1 decade ago
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).
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).
Jaya said:
9 years ago
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.
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.
Gautam said:
1 decade ago
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.
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.
Arpit said:
8 years ago
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?
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?
Nathan said:
7 years ago
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.
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.
Bijata said:
7 years ago
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.
= [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.
Raja ab said:
1 decade ago
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.
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.
Pratik Jadhav said:
4 years ago
How can you add, the interest calculated for the first six months to the principal value to calculate interest for the last six months?
I thought in simple interest we consider only the principal amount and not the interest associated with it from the previous months.
Please clear this to me.
I thought in simple interest we consider only the principal amount and not the interest associated with it from the previous months.
Please clear this to me.
(1)
Purusottam said:
8 years ago
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%.
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%.
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