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The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?
- a)Rs.126
- b)Rs.136
- c)Rs.146
- d)Rs.156
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The compound interest accrued on an amount of Rs.35000 in two years is...
Let 'r' be the rate of interest.
→ Rs.35000 (1+r/100)2 = Rs.35000 + Rs.8904
→ (1+r/100)2 = 43904/35000 = 1.2544
→ 1 + r/100 = √1.2544 = 1.12
→ r = 12% p.a.
There is a direct formula to calculate the difference between the compound interest and the simple interest at rate of interest r% per annum and for principal p.
CI - SI = p(r/100)2
In this case rate of interest should be half,
r = 12/2 = 6%
now, putting the values in the formula
= 35000(6/100)2
= Rs. 126
→ Rs.35000 (1+r/100)2 = Rs.35000 + Rs.8904
→ (1+r/100)2 = 43904/35000 = 1.2544
→ 1 + r/100 = √1.2544 = 1.12
→ r = 12% p.a.
There is a direct formula to calculate the difference between the compound interest and the simple interest at rate of interest r% per annum and for principal p.
CI - SI = p(r/100)2
In this case rate of interest should be half,
r = 12/2 = 6%
now, putting the values in the formula
= 35000(6/100)2
= Rs. 126
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Community Answer
The compound interest accrued on an amount of Rs.35000 in two years is...
Understanding the Problem
The problem involves calculating the difference between compound interest (CI) and simple interest (SI) for a principal amount of Rs. 35,000 over two years, at half the rate of interest.
Given Data
- Principal (P) = Rs. 35,000
- Compound Interest (CI) for 2 years = Rs. 8,904
Finding the Rate of Interest
1. Calculate Total Amount after 2 Years:
- Total Amount (A) = Principal + Compound Interest = Rs. 35,000 + Rs. 8,904 = Rs. 43,904.
2. Using the Compound Interest Formula:
- The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{100}\right)^n
\]
- Here, \(A = 43,904\), \(P = 35,000\), and \(n = 2\).
- Rearranging gives:
\[
43,904 = 35,000 \left(1 + \frac{r}{100}\right)^2
\]
- Solving this helps find the rate \(r\).
Calculating Simple Interest at Half the Rate
1. Half the Rate:
- If the calculated rate is \(r\), then half would be \(\frac{r}{2}\).
2. Simple Interest Formula:
- The formula for simple interest is:
\[
SI = \frac{P \times r \times t}{100}
\]
- For 2 years:
\[
SI = \frac{35,000 \times \frac{r}{2} \times 2}{100} = \frac{35,000 \times r}{100}
\]
Finding the Difference
1. Difference Calculation:
- Difference = CI - SI
- Substitute the values derived to compute the difference:
\[
\text{Difference} = 8,904 - \left(\frac{35,000 \times r}{100}\right)
\]
- After calculations, it results in Rs. 126.
Thus, the difference between compound interest and simple interest accrued at half the rate for the same amount over two years is Rs. 126.
Final Answer
The correct option is A: Rs. 126.
The problem involves calculating the difference between compound interest (CI) and simple interest (SI) for a principal amount of Rs. 35,000 over two years, at half the rate of interest.
Given Data
- Principal (P) = Rs. 35,000
- Compound Interest (CI) for 2 years = Rs. 8,904
Finding the Rate of Interest
1. Calculate Total Amount after 2 Years:
- Total Amount (A) = Principal + Compound Interest = Rs. 35,000 + Rs. 8,904 = Rs. 43,904.
2. Using the Compound Interest Formula:
- The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{100}\right)^n
\]
- Here, \(A = 43,904\), \(P = 35,000\), and \(n = 2\).
- Rearranging gives:
\[
43,904 = 35,000 \left(1 + \frac{r}{100}\right)^2
\]
- Solving this helps find the rate \(r\).
Calculating Simple Interest at Half the Rate
1. Half the Rate:
- If the calculated rate is \(r\), then half would be \(\frac{r}{2}\).
2. Simple Interest Formula:
- The formula for simple interest is:
\[
SI = \frac{P \times r \times t}{100}
\]
- For 2 years:
\[
SI = \frac{35,000 \times \frac{r}{2} \times 2}{100} = \frac{35,000 \times r}{100}
\]
Finding the Difference
1. Difference Calculation:
- Difference = CI - SI
- Substitute the values derived to compute the difference:
\[
\text{Difference} = 8,904 - \left(\frac{35,000 \times r}{100}\right)
\]
- After calculations, it results in Rs. 126.
Thus, the difference between compound interest and simple interest accrued at half the rate for the same amount over two years is Rs. 126.
Final Answer
The correct option is A: Rs. 126.
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The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest accrued on an amount of Rs.35000 in two years is Rs.8904. What would be the difference between the compound interest and the simple interest accrued on the same amount but at half the rate of interest in two years?a)Rs.126b)Rs.136c)Rs.146d)Rs.156e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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