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If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.?
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If the difference between the simple and compound interest compounded ...
Given data:
Principal amount = ?
Rate of interest = 10%
Time = 2 years
Difference between compound and simple interest = Rs. 124.05
Formula:
The formula to calculate the difference between compound and simple interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
\[ CI = A - P \]
\[ SI = P \times r \times t \]
Calculations:
- First, we need to calculate the compound interest using the given data and formula.
- Then, calculate the simple interest using the formula.
- Finally, find the difference between compound interest and simple interest, which is given as Rs. 124.05
Solution:
1. Calculate compound interest:
\[ CI = P \left(1 + \frac{r}{n}\right)^{nt} - P \]
\[ CI = P \left(1 + \frac{0.10}{2}\right)^{2 \times 2} - P \]
\[ CI = P \times (1.05)^4 - P \]
2. Calculate simple interest:
\[ SI = P \times r \times t \]
\[ SI = P \times 0.10 \times 2 \]
3. Find the difference between compound interest and simple interest:
\[ CI - SI = 124.05 \]
\[ P \times (1.05)^4 - P - P \times 0.10 \times 2 = 124.05 \]
4. Solve the equation to find the principal amount (P).
After solving the equation, the principal amount will be obtained.
Principal amount = ?
Rate of interest = 10%
Time = 2 years
Difference between compound and simple interest = Rs. 124.05
Formula:
The formula to calculate the difference between compound and simple interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
\[ CI = A - P \]
\[ SI = P \times r \times t \]
Calculations:
- First, we need to calculate the compound interest using the given data and formula.
- Then, calculate the simple interest using the formula.
- Finally, find the difference between compound interest and simple interest, which is given as Rs. 124.05
Solution:
1. Calculate compound interest:
\[ CI = P \left(1 + \frac{r}{n}\right)^{nt} - P \]
\[ CI = P \left(1 + \frac{0.10}{2}\right)^{2 \times 2} - P \]
\[ CI = P \times (1.05)^4 - P \]
2. Calculate simple interest:
\[ SI = P \times r \times t \]
\[ SI = P \times 0.10 \times 2 \]
3. Find the difference between compound interest and simple interest:
\[ CI - SI = 124.05 \]
\[ P \times (1.05)^4 - P - P \times 0.10 \times 2 = 124.05 \]
4. Solve the equation to find the principal amount (P).
After solving the equation, the principal amount will be obtained.
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If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.?
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If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.? 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 If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.?.
If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.? 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 If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the simple and compound interest compounded every six months at the rate of 10% per annum at the end of 2 years is rupees 124.05. Then, the amount (principal) will be what? Give whole formula.?.
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