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Compound interest on Rs. 40,000 for 4 years at 10% per annum will be 
  • a)
    18000 
  • b)
    17564 
  • c)
    18564 
  • d)
    16000 
Correct answer is option 'C'. Can you explain this answer?
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Understanding Compound Interest
To calculate compound interest, we use the formula:
A = P (1 + r/n)^(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial money).
- r = annual interest rate (decimal).
- n = number of times that interest is compounded per year.
- t = number of years the money is invested or borrowed.
In this case:
- Principal (P) = Rs. 40,000
- Rate (r) = 10% per annum = 0.10
- Time (t) = 4 years
- Compounding frequency (n) = 1 (annually)
Step-by-Step Calculation
1. Calculate the Total Amount (A):
- A = 40000 * (1 + 0.10/1)^(1*4)
- A = 40000 * (1 + 0.10)^4
- A = 40000 * (1.10)^4
- A = 40000 * 1.4641
- A ≈ Rs. 58,564
2. Calculate the Compound Interest (CI):
- CI = A - P
- CI = 58,564 - 40,000
- CI ≈ Rs. 18,564
Conclusion
The compound interest on Rs. 40,000 for 4 years at an annual rate of 10% is approximately Rs. 18,564. Therefore, the correct answer is option 'C'.
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