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A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.
- a)10%
- b)7%
- c)5%
- d)3%
- e)4%
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A sum of money is invested at compound interest at a certain rate. If ...
Let's assume that the principal amount invested is P and the rate of interest is R%.
Compound Interest for 2 years = P * (1 + R/100)^2 - P
Simple Interest for 2 years = 2 * P * R/100
According to the given condition, the simple interest for 2 years is Rs. 20 less than the compound interest for the same number of years. So we have the equation:
2 * P * R/100 = P * (1 + R/100)^2 - P - 20
Simplifying the equation, we get:
2PR/100 = P(1 + 2R/100 + R^2/10000) - P - 20
2PR = P(100 + 2R + R^2/100) - 100P - 2000
2PR = 100P + 2RP + P(R^2/100) - 100P - 2000
2PR = 2RP + P(R^2/100) - 2000
Cancelling out the common terms, we get:
2R = R^2/100 - 1000
Multiplying both sides by 100, we get:
200R = R^2 - 100000
R^2 - 200R - 100000 = 0
Solving this quadratic equation using factorization or the quadratic formula, we find that R = 500 or R = -200.
Since the rate of interest cannot be negative, we discard the solution R = -200.
Therefore, the rate of interest is R = 500%.
But the rate of interest cannot be 500% as it is an unrealistic and extremely high rate. Hence, our assumption that the rate of interest is 500% is incorrect.
We need to re-evaluate our approach and assumptions. Let's consider a different approach.
We know that the simple interest for 3 years is Rs. 61 less than the compound interest for the same number of years.
Compound Interest for 3 years = P * (1 + R/100)^3 - P
Simple Interest for 3 years = 3 * P * R/100
According to the given condition, the simple interest for 3 years is Rs. 61 less than the compound interest for the same number of years. So we have the equation:
3 * P * R/100 = P * (1 + R/100)^3 - P - 61
Simplifying the equation, we get:
3PR/100 = P(1 + 3R/100 + 3R^2/10000 + R^3/1000000) - P - 61
3PR = P(100 + 3R + 3R^2/100 + R^3/10000) - 100P - 6100
3PR = 100P + 3RP + P(3R^2/100 + R^3/10000) - 100P - 6100
3PR = 3RP + P(3R^2/100 + R^3/10000) - 6100
Cancelling out the common terms, we get:
3R = (3R^2/100 + R^3/10000) - 6100
Multiplying both
Compound Interest for 2 years = P * (1 + R/100)^2 - P
Simple Interest for 2 years = 2 * P * R/100
According to the given condition, the simple interest for 2 years is Rs. 20 less than the compound interest for the same number of years. So we have the equation:
2 * P * R/100 = P * (1 + R/100)^2 - P - 20
Simplifying the equation, we get:
2PR/100 = P(1 + 2R/100 + R^2/10000) - P - 20
2PR = P(100 + 2R + R^2/100) - 100P - 2000
2PR = 100P + 2RP + P(R^2/100) - 100P - 2000
2PR = 2RP + P(R^2/100) - 2000
Cancelling out the common terms, we get:
2R = R^2/100 - 1000
Multiplying both sides by 100, we get:
200R = R^2 - 100000
R^2 - 200R - 100000 = 0
Solving this quadratic equation using factorization or the quadratic formula, we find that R = 500 or R = -200.
Since the rate of interest cannot be negative, we discard the solution R = -200.
Therefore, the rate of interest is R = 500%.
But the rate of interest cannot be 500% as it is an unrealistic and extremely high rate. Hence, our assumption that the rate of interest is 500% is incorrect.
We need to re-evaluate our approach and assumptions. Let's consider a different approach.
We know that the simple interest for 3 years is Rs. 61 less than the compound interest for the same number of years.
Compound Interest for 3 years = P * (1 + R/100)^3 - P
Simple Interest for 3 years = 3 * P * R/100
According to the given condition, the simple interest for 3 years is Rs. 61 less than the compound interest for the same number of years. So we have the equation:
3 * P * R/100 = P * (1 + R/100)^3 - P - 61
Simplifying the equation, we get:
3PR/100 = P(1 + 3R/100 + 3R^2/10000 + R^3/1000000) - P - 61
3PR = P(100 + 3R + 3R^2/100 + R^3/10000) - 100P - 6100
3PR = 100P + 3RP + P(3R^2/100 + R^3/10000) - 100P - 6100
3PR = 3RP + P(3R^2/100 + R^3/10000) - 6100
Cancelling out the common terms, we get:
3R = (3R^2/100 + R^3/10000) - 6100
Multiplying both
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Community Answer
A sum of money is invested at compound interest at a certain rate. If ...
Let principal = P. rate = R
According to question,
For 2 years,
C.I. - S.I. = 20
For 3 years,
C.I. - S.I. = 61
Dividing (1) and (2), we get
R = 5%
According to question,
For 2 years,
C.I. - S.I. = 20
For 3 years,
C.I. - S.I. = 61
Dividing (1) and (2), we get
R = 5%
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A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.a)10%b)7%c)5%d)3%e)4%Correct answer is option 'C'. Can you explain this answer?
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A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.a)10%b)7%c)5%d)3%e)4%Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.a)10%b)7%c)5%d)3%e)4%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.a)10%b)7%c)5%d)3%e)4%Correct answer is option 'C'. Can you explain this answer?.
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