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Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?
- a)Rs 10,000
- b)Rs 8,000
- c)Rs 12,000
- d)Rs 14,000
Correct answer is option 'B'. Can you explain this answer?
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Difference is 30 - The difference between the simple and the compound ...
To solve this problem, we need to calculate the difference between the simple interest and the compound interest compounded every six months at a rate of 10% per annum.
Let's assume the principal sum is 'P'.
Simple Interest
The simple interest on a principal amount 'P' at a rate of 10% per annum for 2 years is given by the formula:
SI = (P * R * T)/100
Where:
P = Principal amount
R = Rate of interest
T = Time period
In this case, the simple interest would be:
SI = (P * 10 * 2)/100 = (P * 20)/100 = 0.2P
Compound Interest
The compound interest compounded every six months at a rate of 10% per annum for 2 years can be calculated using the formula:
CI = P * (1 + R/100)^n - P
Where:
P = Principal amount
R = Rate of interest
n = Number of compounding periods
Since the interest is compounded every six months, the number of compounding periods over 2 years would be 2*2 = 4.
In this case, the compound interest would be:
CI = P * (1 + 10/100)^4 - P = P * (1.1)^4 - P
Difference between Simple Interest and Compound Interest
The difference between the compound interest and the simple interest can be calculated as:
Difference = CI - SI = [P * (1.1)^4 - P] - 0.2P
Difference = P * (1.1^4 - 1) - 0.2P
Given that the difference is Rs. 124.05, we can write the equation as:
124.05 = P * (1.1^4 - 1) - 0.2P
Solving for P:
124.05 = P * (1.4641 - 1) - 0.2P
124.05 = 0.4641P - 0.2P
124.05 = 0.2641P
P = 124.05 / 0.2641
P ≈ Rs. 470.24
Therefore, the principal sum is approximately Rs. 470.24.
Now, we need to find the closest option to Rs. 470.24.
The closest option is Rs. 8,000 (option B).
Thus, the sum is Rs. 8,000.
Let's assume the principal sum is 'P'.
Simple Interest
The simple interest on a principal amount 'P' at a rate of 10% per annum for 2 years is given by the formula:
SI = (P * R * T)/100
Where:
P = Principal amount
R = Rate of interest
T = Time period
In this case, the simple interest would be:
SI = (P * 10 * 2)/100 = (P * 20)/100 = 0.2P
Compound Interest
The compound interest compounded every six months at a rate of 10% per annum for 2 years can be calculated using the formula:
CI = P * (1 + R/100)^n - P
Where:
P = Principal amount
R = Rate of interest
n = Number of compounding periods
Since the interest is compounded every six months, the number of compounding periods over 2 years would be 2*2 = 4.
In this case, the compound interest would be:
CI = P * (1 + 10/100)^4 - P = P * (1.1)^4 - P
Difference between Simple Interest and Compound Interest
The difference between the compound interest and the simple interest can be calculated as:
Difference = CI - SI = [P * (1.1)^4 - P] - 0.2P
Difference = P * (1.1^4 - 1) - 0.2P
Given that the difference is Rs. 124.05, we can write the equation as:
124.05 = P * (1.1^4 - 1) - 0.2P
Solving for P:
124.05 = P * (1.4641 - 1) - 0.2P
124.05 = 0.4641P - 0.2P
124.05 = 0.2641P
P = 124.05 / 0.2641
P ≈ Rs. 470.24
Therefore, the principal sum is approximately Rs. 470.24.
Now, we need to find the closest option to Rs. 470.24.
The closest option is Rs. 8,000 (option B).
Thus, the sum is Rs. 8,000.
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Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer?
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Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer?.
Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer?.
Solutions for Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
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Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Difference is 30 - The difference between the simple and the compound interest compounded every six rnonths at the rate of 10 %.p.a. at the end of two years is Rs. 124.05. What is the sum?a)Rs 10,000b)Rs 8,000c)Rs 12,000d)Rs 14,000Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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