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The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.?
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The difference between the compound interest and the simple interest o...
Understanding the Problem
To find the sum (principal), we need to understand the relationship between compound interest (CI) and simple interest (SI). The difference between CI and SI over 3 years at a rate of 10% is given as 93 rupees.
Formulas for Interest
- Simple Interest (SI) = P * r * t / 100
- Compound Interest (CI) = P * (1 + r/100)^t - P
Where:
P = Principal amount
r = Rate of interest (10%)
t = Time (3 years)
Difference between CI and SI
The difference between compound interest and simple interest over 3 years is calculated as follows:
- Difference = CI - SI = P * [(1 + r/100)^t - 1] - P * (r * t / 100)
This simplifies to:
- Difference = P * [(1 + 0.1)^3 - 1 - (0.1 * 3)]
Calculating the Difference
1. Calculate (1 + 0.1)^3:
- (1.1)^3 = 1.331
2. Now, substitute this value into the difference formula:
- Difference = P * [1.331 - 1 - 0.3]
- Difference = P * [0.031]
3. Set the difference to 93 rupees:
- P * 0.031 = 93
Finding the Principal Amount
To find P:
- P = 93 / 0.031
- P = 3000
Conclusion
The sum (principal) is 3000 rupees. This demonstrates the impact of compound interest over simple interest over a period of 3 years at a rate of 10%.
To find the sum (principal), we need to understand the relationship between compound interest (CI) and simple interest (SI). The difference between CI and SI over 3 years at a rate of 10% is given as 93 rupees.
Formulas for Interest
- Simple Interest (SI) = P * r * t / 100
- Compound Interest (CI) = P * (1 + r/100)^t - P
Where:
P = Principal amount
r = Rate of interest (10%)
t = Time (3 years)
Difference between CI and SI
The difference between compound interest and simple interest over 3 years is calculated as follows:
- Difference = CI - SI = P * [(1 + r/100)^t - 1] - P * (r * t / 100)
This simplifies to:
- Difference = P * [(1 + 0.1)^3 - 1 - (0.1 * 3)]
Calculating the Difference
1. Calculate (1 + 0.1)^3:
- (1.1)^3 = 1.331
2. Now, substitute this value into the difference formula:
- Difference = P * [1.331 - 1 - 0.3]
- Difference = P * [0.031]
3. Set the difference to 93 rupees:
- P * 0.031 = 93
Finding the Principal Amount
To find P:
- P = 93 / 0.031
- P = 3000
Conclusion
The sum (principal) is 3000 rupees. This demonstrates the impact of compound interest over simple interest over a period of 3 years at a rate of 10%.
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The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.?
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The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.?.
The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is rupees 93. Find the sum.?.
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