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On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164?
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On what sum will the compound interest at 5% per annum for 2 years com...
Understanding the Problem
To find the principal sum (P) on which the compound interest (CI) at 5% per annum for 2 years is rupees 164, we can use the formula for compound interest.
Compound Interest Formula
The formula for compound interest is:
CI = P * (1 + r/n)^(nt) - P
Where:
- CI = Compound Interest
- P = Principal amount (initial sum)
- r = Annual interest rate (decimal)
- n = Number of times interest applied per time period
- t = Number of time periods the money is invested or borrowed for
Since the interest is compounded annually, n = 1.
Parameters for Our Calculation
- CI = 164
- r = 5/100 = 0.05
- n = 1
- t = 2
Rearranging the Formula
We can rearrange the compound interest formula to find P:
P = CI / ((1 + r)^t - 1)
Calculating Principal (P)
Now, plug in the values:
1. Calculate (1 + r):
- 1 + 0.05 = 1.05
2. Raise it to the power of t:
- (1.05)^2 = 1.1025
3. Subtract 1:
- 1.1025 - 1 = 0.1025
4. Now, divide CI by this result:
- P = 164 / 0.1025 ≈ 1600
Conclusion
The principal sum on which the compound interest at 5% per annum for 2 years amounts to rupees 164 is approximately:
Rupees 1600
To find the principal sum (P) on which the compound interest (CI) at 5% per annum for 2 years is rupees 164, we can use the formula for compound interest.
Compound Interest Formula
The formula for compound interest is:
CI = P * (1 + r/n)^(nt) - P
Where:
- CI = Compound Interest
- P = Principal amount (initial sum)
- r = Annual interest rate (decimal)
- n = Number of times interest applied per time period
- t = Number of time periods the money is invested or borrowed for
Since the interest is compounded annually, n = 1.
Parameters for Our Calculation
- CI = 164
- r = 5/100 = 0.05
- n = 1
- t = 2
Rearranging the Formula
We can rearrange the compound interest formula to find P:
P = CI / ((1 + r)^t - 1)
Calculating Principal (P)
Now, plug in the values:
1. Calculate (1 + r):
- 1 + 0.05 = 1.05
2. Raise it to the power of t:
- (1.05)^2 = 1.1025
3. Subtract 1:
- 1.1025 - 1 = 0.1025
4. Now, divide CI by this result:
- P = 164 / 0.1025 ≈ 1600
Conclusion
The principal sum on which the compound interest at 5% per annum for 2 years amounts to rupees 164 is approximately:
Rupees 1600
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On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164?
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On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164?.
On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On what sum will the compound interest at 5% per annum for 2 years compound annually be ruppes 164?.
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