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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
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
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
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The difference between the simple interest and compound interest earne...
To solve this question, we need to first calculate the simple interest and compound interest earned on the sum placed for two years at 8% using the given information.
Let's assume the principal amount is P.
The simple interest earned can be calculated using the formula:
Simple Interest = (P * R * T) / 100
Given that the simple interest and compound interest difference is Rs.30.72, we have:
Simple Interest - Compound Interest = Rs.30.72
Now, let's calculate the simple interest earned for 2 years at 8%:
Simple Interest = (P * 8 * 2) / 100 = (16P) / 100 = 0.16P
Next, let's calculate the compound interest earned on the sum placed for two years at 8% compounded annually.
The compound interest formula is:
Compound Interest = P * (1 + R/100)^T - P
For two years at 8% compounded annually:
Compound Interest = P * (1 + 8/100)^2 - P = P * (1.08)^2 - P = 1.1664P - P = 0.1664P
Now, we can substitute the values in the equation:
Simple Interest - Compound Interest = Rs.30.72
0.16P - 0.1664P = Rs.30.72
-0.0064P = Rs.30.72
P = Rs.30.72 / -0.0064 ≈ Rs.4800
Now that we have the principal amount, we can calculate the compound interest earned when the interest is compounded on a half-yearly basis.
The formula for compound interest compounded half-yearly is:
Compound Interest = P * (1 + R/200)^(2*T) - P
For two years at 8% compounded half-yearly:
Compound Interest = 4800 * (1 + 8/200)^(2*2) - 4800 ≈ 4800 * 1.0816^4 - 4800 ≈ 4800 * 1.373665536 - 4800 ≈ 6583.19 - 4800 ≈ Rs.1783.19
Now, we can calculate the difference between the two compound interests:
Difference in Compound Interest = Rs.1783.19 - Rs.0.1664P
≈ Rs.1783.19 - Rs.0.1664*4800
≈ Rs.1783.19 - Rs.797.76
≈ Rs.985.43
Therefore, the difference in the two interest amounts, when the interest is compounded on a half-yearly basis, is approximately Rs.985.43, which is closest to option C (Rs.47.32).
Let's assume the principal amount is P.
The simple interest earned can be calculated using the formula:
Simple Interest = (P * R * T) / 100
Given that the simple interest and compound interest difference is Rs.30.72, we have:
Simple Interest - Compound Interest = Rs.30.72
Now, let's calculate the simple interest earned for 2 years at 8%:
Simple Interest = (P * 8 * 2) / 100 = (16P) / 100 = 0.16P
Next, let's calculate the compound interest earned on the sum placed for two years at 8% compounded annually.
The compound interest formula is:
Compound Interest = P * (1 + R/100)^T - P
For two years at 8% compounded annually:
Compound Interest = P * (1 + 8/100)^2 - P = P * (1.08)^2 - P = 1.1664P - P = 0.1664P
Now, we can substitute the values in the equation:
Simple Interest - Compound Interest = Rs.30.72
0.16P - 0.1664P = Rs.30.72
-0.0064P = Rs.30.72
P = Rs.30.72 / -0.0064 ≈ Rs.4800
Now that we have the principal amount, we can calculate the compound interest earned when the interest is compounded on a half-yearly basis.
The formula for compound interest compounded half-yearly is:
Compound Interest = P * (1 + R/200)^(2*T) - P
For two years at 8% compounded half-yearly:
Compound Interest = 4800 * (1 + 8/200)^(2*2) - 4800 ≈ 4800 * 1.0816^4 - 4800 ≈ 4800 * 1.373665536 - 4800 ≈ 6583.19 - 4800 ≈ Rs.1783.19
Now, we can calculate the difference between the two compound interests:
Difference in Compound Interest = Rs.1783.19 - Rs.0.1664P
≈ Rs.1783.19 - Rs.0.1664*4800
≈ Rs.1783.19 - Rs.797.76
≈ Rs.985.43
Therefore, the difference in the two interest amounts, when the interest is compounded on a half-yearly basis, is approximately Rs.985.43, which is closest to option C (Rs.47.32).
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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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