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The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year is
- a)Rs. 48
- b)Rs. 66.56
- c)Rs. 98.56
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The compound interest on a sum of money for 2 years is Rs. 832 and the...
Difference in Cl and SI in second year = Rs 32
Cl = SI for fist year = 800/2 = 400
This difference of Rs. 32 is the SI earned on Rs. 400 on one year (as the SI on first year is also added to principal for second year).
r = [(100 x 32)/(400 x 1)] = 8%
Difference between Cl and SI for 3rd year = SI on Rs. 832 for one year
= (832 x 1 x 8)/100
= Rs 66.56
Hence, option 2.
Cl = SI for fist year = 800/2 = 400
This difference of Rs. 32 is the SI earned on Rs. 400 on one year (as the SI on first year is also added to principal for second year).
r = [(100 x 32)/(400 x 1)] = 8%
Difference between Cl and SI for 3rd year = SI on Rs. 832 for one year
= (832 x 1 x 8)/100
= Rs 66.56
Hence, option 2.
Most Upvoted Answer
The compound interest on a sum of money for 2 years is Rs. 832 and the...
Given:
Compound interest for 2 years = Rs. 832
Simple interest for 2 years = Rs. 800
To find:
Difference between compound interest and simple interest for the third year
Solution:
Let's assume the principal amount is P and the rate of interest is R%.
Calculating Compound Interest:
Compound interest for 2 years = P * (1 + R/100)^2 - P
Given, compound interest for 2 years = Rs. 832
So,
P * (1 + R/100)^2 - P = 832
P * (1 + R/100)^2 = P + 832
(1 + R/100)^2 = 1 + 832/P
Calculating Simple Interest:
Simple interest for 2 years = P * R * 2/100
Given, simple interest for 2 years = Rs. 800
So,
P * R * 2/100 = 800
P * R/100 = 400
Calculating Difference between Compound Interest and Simple Interest for the Third Year:
To find the difference between the compound interest and simple interest for the third year, we need to calculate the compound interest and simple interest for the third year separately.
Compound Interest for the Third Year:
Compound interest for 3 years = P * (1 + R/100)^3 - P
Compound interest for the third year = P * (1 + R/100)^3 - P - (P * (1 + R/100)^2 - P)
Compound interest for the third year = P * (1 + R/100)^3 - P * (1 + R/100)^2
Compound interest for the third year = P * (1 + R/100)^2 * ((1 + R/100) - 1)
Compound interest for the third year = P * (1 + R/100)^2 * (1 + R/100 - 1)
Compound interest for the third year = P * (1 + R/100)^2 * (R/100)
Simple Interest for the Third Year:
Simple interest for 3 years = P * R * 3/100
Simple interest for the third year = P * R * 3/100 - P * R * 2/100
Simple interest for the third year = P * R/100 * (3 - 2)
Simple interest for the third year = P * R/100
Calculating the Difference:
Difference between the compound interest and simple interest for the third year = Compound interest for the third year - Simple interest for the third year
Difference between the compound interest and simple interest for the third year = P * (1 + R/100)^2 * (R/100) - P * R/100
Difference between the compound interest and simple interest for the third year = P * R/100 * ((1 + R/100)^2 - 1)
From the given options, the answer is option B) Rs. 66.56.
Compound interest for 2 years = Rs. 832
Simple interest for 2 years = Rs. 800
To find:
Difference between compound interest and simple interest for the third year
Solution:
Let's assume the principal amount is P and the rate of interest is R%.
Calculating Compound Interest:
Compound interest for 2 years = P * (1 + R/100)^2 - P
Given, compound interest for 2 years = Rs. 832
So,
P * (1 + R/100)^2 - P = 832
P * (1 + R/100)^2 = P + 832
(1 + R/100)^2 = 1 + 832/P
Calculating Simple Interest:
Simple interest for 2 years = P * R * 2/100
Given, simple interest for 2 years = Rs. 800
So,
P * R * 2/100 = 800
P * R/100 = 400
Calculating Difference between Compound Interest and Simple Interest for the Third Year:
To find the difference between the compound interest and simple interest for the third year, we need to calculate the compound interest and simple interest for the third year separately.
Compound Interest for the Third Year:
Compound interest for 3 years = P * (1 + R/100)^3 - P
Compound interest for the third year = P * (1 + R/100)^3 - P - (P * (1 + R/100)^2 - P)
Compound interest for the third year = P * (1 + R/100)^3 - P * (1 + R/100)^2
Compound interest for the third year = P * (1 + R/100)^2 * ((1 + R/100) - 1)
Compound interest for the third year = P * (1 + R/100)^2 * (1 + R/100 - 1)
Compound interest for the third year = P * (1 + R/100)^2 * (R/100)
Simple Interest for the Third Year:
Simple interest for 3 years = P * R * 3/100
Simple interest for the third year = P * R * 3/100 - P * R * 2/100
Simple interest for the third year = P * R/100 * (3 - 2)
Simple interest for the third year = P * R/100
Calculating the Difference:
Difference between the compound interest and simple interest for the third year = Compound interest for the third year - Simple interest for the third year
Difference between the compound interest and simple interest for the third year = P * (1 + R/100)^2 * (R/100) - P * R/100
Difference between the compound interest and simple interest for the third year = P * R/100 * ((1 + R/100)^2 - 1)
From the given options, the answer is option B) Rs. 66.56.
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Community Answer
The compound interest on a sum of money for 2 years is Rs. 832 and the...
Rate of interest is 8% so s. I. 1200 but c. I. will be 1200 + 32+32+2.56
the difference between c. I. and s. I. is 66.56
the difference between c. I. and s. I. is 66.56
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The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. 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 The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. 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 The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and simple interest for the third year isa)Rs. 48b)Rs. 66.56c)Rs. 98.56d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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