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A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?
- a)Rs 25,600
- b)Rs 20,000
- c)Rs 26,040
- d)Rs 40,500
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A sum of money is lent for 2 years at 20% p.a. compound interest. It y...
P[1 + (r/2)/100]4 – P[1 + r/100]2 = 482
P[1 + 10/100]4 – P[1 + 20/100]2 = 482
Solve, P = 20,000
P[1 + 10/100]4 – P[1 + 20/100]2 = 482
Solve, P = 20,000
Most Upvoted Answer
A sum of money is lent for 2 years at 20% p.a. compound interest. It y...
P[1 + (r/2)/100]4 – P[1 + r/100]2 = 482
P[1 + 10/100]4 – P[1 + 20/100]2 = 482
Solve, P = 20,000
P[1 + 10/100]4 – P[1 + 20/100]2 = 482
Solve, P = 20,000
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Community Answer
A sum of money is lent for 2 years at 20% p.a. compound interest. It y...
Given information:
- The money is lent for 2 years.
- The interest rate is 20% per annum.
- The interest is compounded annually and semi-annually.
- The interest earned when compounded semi-annually is Rs 482 more than when compounded annually.
To find:
The sum of money lent.
Solution:
Let's assume the sum of money lent is Rs X.
When interest is compounded annually:
- The principal amount after 2 years will be X(1 + 20/100)^2 = X(6/5)^2 = X(36/25).
- The interest earned will be X(36/25) - X = 36X/25 - X = 11X/25.
When interest is compounded semi-annually:
- The principal amount after 2 years will be X(1 + 20/100/2)^(2*2) = X(1 + 1/10)^4 = X(11/10)^4 = X(14641/10000).
- The interest earned will be X(14641/10000) - X = 4641X/10000.
According to the given condition, the interest earned when compounded semi-annually is Rs 482 more than when compounded annually.
So, we have the equation: 4641X/10000 - 11X/25 = 482.
Solving the equation:
Let's simplify the equation and solve for X:
4641X/10000 - 11X/25 = 482
(4641X*25 - 11X*10000)/(10000*25) = 482
(116025X - 110000X)/250000 = 482
(601025X - 110000X) = 482 * 250000
491025X = 482 * 250000
X = (482 * 250000)/491025
X ≈ Rs 2458.20
Therefore, the sum of money lent is approximately Rs 2458.20.
Conclusion:
The correct option is (e) None of these, as the given options do not include the answer we obtained (Rs 2458.20).
- The money is lent for 2 years.
- The interest rate is 20% per annum.
- The interest is compounded annually and semi-annually.
- The interest earned when compounded semi-annually is Rs 482 more than when compounded annually.
To find:
The sum of money lent.
Solution:
Let's assume the sum of money lent is Rs X.
When interest is compounded annually:
- The principal amount after 2 years will be X(1 + 20/100)^2 = X(6/5)^2 = X(36/25).
- The interest earned will be X(36/25) - X = 36X/25 - X = 11X/25.
When interest is compounded semi-annually:
- The principal amount after 2 years will be X(1 + 20/100/2)^(2*2) = X(1 + 1/10)^4 = X(11/10)^4 = X(14641/10000).
- The interest earned will be X(14641/10000) - X = 4641X/10000.
According to the given condition, the interest earned when compounded semi-annually is Rs 482 more than when compounded annually.
So, we have the equation: 4641X/10000 - 11X/25 = 482.
Solving the equation:
Let's simplify the equation and solve for X:
4641X/10000 - 11X/25 = 482
(4641X*25 - 11X*10000)/(10000*25) = 482
(116025X - 110000X)/250000 = 482
(601025X - 110000X) = 482 * 250000
491025X = 482 * 250000
X = (482 * 250000)/491025
X ≈ Rs 2458.20
Therefore, the sum of money lent is approximately Rs 2458.20.
Conclusion:
The correct option is (e) None of these, as the given options do not include the answer we obtained (Rs 2458.20).
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A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?a)Rs 25,600b)Rs 20,000c)Rs 26,040d)Rs 40,500e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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