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A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.
- a)Rs. 7,000
- b)Rs. 7,200
- c)Rs. 7,500
- d)Rs. 7,700
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A certain sum, invested at 4% per annum at compound interest, compoun...
Let the sum be Rs. P.
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As the interest is compounded half-yearly,
∴ R = 2% T, = 2 half years
Alternatively:-
If interest is compounded half-yearly rate will be 2%
C.l. for 2 years = 4.04%
Most Upvoted Answer
A certain sum, invested at 4% per annum at compound interest, compoun...
To find the initial sum, we can use the formula for compound interest:
\[A = P(1 + r/n)^(nt)\]
Where:
- A is the final amount
- P is the principal sum (initial amount)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the final amount A is given as Rs. 7,803, the interest rate r is 4% (or 0.04), and the interest is compounded half-yearly, so n = 2. The time t is given as 1 year.
Substituting the known values into the formula, we get:
\[7,803 = P(1 + 0.04/2)^(2*1)\]
Simplifying further:
\[7,803 = P(1 + 0.02)^2\]
\[7,803 = P(1.02)^2\]
\[7,803 = P(1.0404)\]
Dividing both sides of the equation by 1.0404:
\[P = \frac{7,803}{1.0404}\]
\[P \approx 7,500\]
Therefore, the initial sum (principal amount) is approximately Rs. 7,500. Hence, option C is the correct answer.
\[A = P(1 + r/n)^(nt)\]
Where:
- A is the final amount
- P is the principal sum (initial amount)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the final amount A is given as Rs. 7,803, the interest rate r is 4% (or 0.04), and the interest is compounded half-yearly, so n = 2. The time t is given as 1 year.
Substituting the known values into the formula, we get:
\[7,803 = P(1 + 0.04/2)^(2*1)\]
Simplifying further:
\[7,803 = P(1 + 0.02)^2\]
\[7,803 = P(1.02)^2\]
\[7,803 = P(1.0404)\]
Dividing both sides of the equation by 1.0404:
\[P = \frac{7,803}{1.0404}\]
\[P \approx 7,500\]
Therefore, the initial sum (principal amount) is approximately Rs. 7,500. Hence, option C is the correct answer.
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A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. Can you explain this answer?
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A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. 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 A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. Can you explain this answer?.
A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. 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 A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs. 7,803 at the end of one year. Find the sum.a)Rs. 7,000b)Rs. 7,200c)Rs. 7,500d)Rs. 7,700Correct answer is option 'C'. Can you explain this answer?.
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