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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%.
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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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