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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...
If interest is compounded half-yearly rate will be 2 %
C.I. for 2 years = 4.04%
Principal = 7803 / 104.04 x 100
= Rs.7500
Most Upvoted Answer
A certain sum, invested at 4% per annum at compound interest, compoun...
Understanding Compound Interest
To find the principal sum (P) that amounts to Rs. 7,803 after one year at a 4% annual interest rate compounded half-yearly, we can utilize the compound interest formula:
Formula
The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- A = the amount after time t
- P = principal amount (initial sum)
- r = annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = number of years
Given Values
- A = Rs. 7,803
- r = 4% per annum = 0.04
- n = 2 (since it is compounded half-yearly)
- t = 1 year
Calculating the Principal
Substituting the values into the formula, we have:
\[ 7803 = P \left(1 + \frac{0.04}{2}\right)^{2 \times 1} \]
This simplifies to:
\[ 7803 = P \left(1 + 0.02\right)^{2} \]
\[ 7803 = P (1.02)^{2} \]
Calculating \( (1.02)^{2} \):
\[ (1.02)^{2} = 1.0404 \]
Now substitute this back into the equation:
\[ 7803 = P \cdot 1.0404 \]
To find P:
\[ P = \frac{7803}{1.0404} \approx 7500 \]
Conclusion
Hence, the principal sum invested is approximately Rs. 7,500. Thus, the correct answer is option 'C' (Rs. 7,500).
To find the principal sum (P) that amounts to Rs. 7,803 after one year at a 4% annual interest rate compounded half-yearly, we can utilize the compound interest formula:
Formula
The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- A = the amount after time t
- P = principal amount (initial sum)
- r = annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = number of years
Given Values
- A = Rs. 7,803
- r = 4% per annum = 0.04
- n = 2 (since it is compounded half-yearly)
- t = 1 year
Calculating the Principal
Substituting the values into the formula, we have:
\[ 7803 = P \left(1 + \frac{0.04}{2}\right)^{2 \times 1} \]
This simplifies to:
\[ 7803 = P \left(1 + 0.02\right)^{2} \]
\[ 7803 = P (1.02)^{2} \]
Calculating \( (1.02)^{2} \):
\[ (1.02)^{2} = 1.0404 \]
Now substitute this back into the equation:
\[ 7803 = P \cdot 1.0404 \]
To find P:
\[ P = \frac{7803}{1.0404} \approx 7500 \]
Conclusion
Hence, the principal sum invested is approximately Rs. 7,500. Thus, the correct answer is option 'C' (Rs. 7,500).
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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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