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The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?
- a)Rs. 16.62
- b)Rs. 17.82
- c)Rs. 47.32
- d)Rs. 42.72
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The difference between the simple interest and compound interest earne...
Consider annual compounding.
Interest for the first year is the same, irrespective of whether it is simple interest or compound interest.
Hence, the difference between the two interest amounts is due to the extra compound interest earned in the second year.
The C.l. earned in the first year is added to the original principal and this sum becomes the principal for the second year.
Hence, the situation is equivalent to placing (original principal + C.l. of first year (say x)) at 8% simple interest for one year.
Hence, effectively, Rs.30.72 is the simple interest earned by placing Rs. x at 8% S.l. for a year 30.72 = x(0.08) x = 384
This is also the S.l. earned by keeping the original principal at 8% for a year
Original principal = 384/0.08 = 4800 Hence, at half-yearly compounding, amount due at the end of 2 years = 4800[1 + (4/100)]4 = 5615.32
Interest for the first year is the same, irrespective of whether it is simple interest or compound interest.
Hence, the difference between the two interest amounts is due to the extra compound interest earned in the second year.
The C.l. earned in the first year is added to the original principal and this sum becomes the principal for the second year.
Hence, the situation is equivalent to placing (original principal + C.l. of first year (say x)) at 8% simple interest for one year.
Hence, effectively, Rs.30.72 is the simple interest earned by placing Rs. x at 8% S.l. for a year 30.72 = x(0.08) x = 384
This is also the S.l. earned by keeping the original principal at 8% for a year
Original principal = 384/0.08 = 4800 Hence, at half-yearly compounding, amount due at the end of 2 years = 4800[1 + (4/100)]4 = 5615.32
C.l. = 5615.32 - 4800 = Rs. 815.32
S.l. for Rs.4,800 at 8% for 2 years = (4800 x 8 x 2)/100 = Rs. 768
Required difference = 815.32 - 768 = Rs. 47.32
Hence, option 3.
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Difference between Simple Interest and Compound Interest:
To understand the concept of simple interest and compound interest, let's first define them:
- Simple Interest: Simple interest is calculated only on the principal amount for a specific period of time. It does not take into account any interest that has been previously earned.
- Compound Interest: Compound interest is calculated on both the principal amount and the interest that has been previously earned. It is calculated at regular intervals, usually annually, semi-annually, quarterly, or monthly.
Given Information:
Principal amount (P) = ? (not given)
Rate of interest (R) = 8%
Time period (T) = 2 years
Difference in interest amounts (Simple Interest - Compound Interest) = Rs. 30.72
Calculation of Simple Interest:
Simple Interest (SI) = (P * R * T) / 100
30.72 = (P * 8 * 2) / 100
P = (30.72 * 100) / (8 * 2)
P = Rs. 192
Calculation of Compound Interest (Annually):
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = 192 * (1 + 8/100)^2 - 192
CI = 192 * (1.08)^2 - 192
CI = 192 * 1.1664 - 192
CI = 223.54 - 192
CI = Rs. 31.54
Calculation of Compound Interest (Half-Yearly):
As the interest is compounded half-yearly, the rate of interest (R) will be divided by 2, and the time period (T) will be multiplied by 2.
Compound Interest (CI) = P * (1 + R/200)^(2T) - P
CI = 192 * (1 + 8/200)^(2*2) - 192
CI = 192 * (1.04)^4 - 192
CI = 192 * 1.16985856 - 192
CI = 224.71 - 192
CI = Rs. 32.71
Calculation of Difference in Compound Interest:
Difference in Compound Interest = CI (Half-Yearly) - CI (Annually)
Difference = 32.71 - 31.54
Difference ≈ Rs. 1.17
Therefore, the approximate difference in the two interest amounts when compounded half-yearly is Rs. 1.17.
Conclusion:
The difference in the interest amounts when compounded half-yearly is approximately Rs. 1.17.
To understand the concept of simple interest and compound interest, let's first define them:
- Simple Interest: Simple interest is calculated only on the principal amount for a specific period of time. It does not take into account any interest that has been previously earned.
- Compound Interest: Compound interest is calculated on both the principal amount and the interest that has been previously earned. It is calculated at regular intervals, usually annually, semi-annually, quarterly, or monthly.
Given Information:
Principal amount (P) = ? (not given)
Rate of interest (R) = 8%
Time period (T) = 2 years
Difference in interest amounts (Simple Interest - Compound Interest) = Rs. 30.72
Calculation of Simple Interest:
Simple Interest (SI) = (P * R * T) / 100
30.72 = (P * 8 * 2) / 100
P = (30.72 * 100) / (8 * 2)
P = Rs. 192
Calculation of Compound Interest (Annually):
Compound Interest (CI) = P * (1 + R/100)^T - P
CI = 192 * (1 + 8/100)^2 - 192
CI = 192 * (1.08)^2 - 192
CI = 192 * 1.1664 - 192
CI = 223.54 - 192
CI = Rs. 31.54
Calculation of Compound Interest (Half-Yearly):
As the interest is compounded half-yearly, the rate of interest (R) will be divided by 2, and the time period (T) will be multiplied by 2.
Compound Interest (CI) = P * (1 + R/200)^(2T) - P
CI = 192 * (1 + 8/200)^(2*2) - 192
CI = 192 * (1.04)^4 - 192
CI = 192 * 1.16985856 - 192
CI = 224.71 - 192
CI = Rs. 32.71
Calculation of Difference in Compound Interest:
Difference in Compound Interest = CI (Half-Yearly) - CI (Annually)
Difference = 32.71 - 31.54
Difference ≈ Rs. 1.17
Therefore, the approximate difference in the two interest amounts when compounded half-yearly is Rs. 1.17.
Conclusion:
The difference in the interest amounts when compounded half-yearly is approximately Rs. 1.17.
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The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct answer is option 'C'. Can you explain this answer?
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The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct 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 The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct 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 The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct answer is option 'C'. Can you explain this answer?.
The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct 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 The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct 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 The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a half-yearly basis, what would the difference in the two interest amount approximately be?a)Rs. 16.62b)Rs. 17.82c)Rs. 47.32d)Rs. 42.72Correct answer is option 'C'. Can you explain this answer?.
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