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The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?
- a)Rs. 6,000
- b)Rs. 4,800
- c)Rs. 3,600
- d)Rs. 2,400
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The difference between the compound interest (compounded annually) and...
Difference in the CI and SI for 2 years = Simple interest on the simple interest earned in first year
⇒ 15 = Rate/100 × Time × Simple interest earned in first year
⇒ 15 = 5/100 × 1 × Simple interest earned in first year
∴ Simple interest earned in first year = 300
Principal × Rate/100 × Time = 300
⇒ Principal × 5/100 × 1 = 300
∴ Principal = Rs. 6000
⇒ 15 = Rate/100 × Time × Simple interest earned in first year
⇒ 15 = 5/100 × 1 × Simple interest earned in first year
∴ Simple interest earned in first year = 300
Principal × Rate/100 × Time = 300
⇒ Principal × 5/100 × 1 = 300
∴ Principal = Rs. 6000
Most Upvoted Answer
The difference between the compound interest (compounded annually) and...
Understanding Interest Types
When you deposit money in a bank, you can earn interest in two ways: simple interest (SI) and compound interest (CI). The difference between these two types of interest can help us find the sum of money deposited.
Formulas for Interest Calculation
- Simple Interest (SI):
\[ SI = \frac{P \times R \times T}{100} \]
where P = principal amount, R = rate of interest per annum, T = time in years.
- Compound Interest (CI):
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
This can also be expressed as:
\[ CI = P \times \left(1 + \frac{R}{100}\right)^T - P \]
Given Information
- Rate of interest (R) = 5%
- Time (T) = 2 years
- Difference between CI and SI = Rs. 15
Calculating Simple Interest (SI)
For 2 years:
\[ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]
Calculating Compound Interest (CI)
For 2 years:
\[ CI = P \left(1 + \frac{5}{100}\right)^2 - P \]
\[ CI = P \left(1.05^2\right) - P = P \left(1.1025 - 1\right) = 0.1025P \]
Finding the Difference
Now, we can find the difference:
\[ CI - SI = 0.1025P - \frac{P}{10} = 15 \]
Convert \(\frac{P}{10}\) to a decimal:
\[ 0.1025P - 0.1P = 15 \]
\[ 0.0025P = 15 \]
\[ P = \frac{15}{0.0025} = 6000 \]
Conclusion
The sum of money deposited is Rs. 6,000, which corresponds to option 'A'.
When you deposit money in a bank, you can earn interest in two ways: simple interest (SI) and compound interest (CI). The difference between these two types of interest can help us find the sum of money deposited.
Formulas for Interest Calculation
- Simple Interest (SI):
\[ SI = \frac{P \times R \times T}{100} \]
where P = principal amount, R = rate of interest per annum, T = time in years.
- Compound Interest (CI):
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
This can also be expressed as:
\[ CI = P \times \left(1 + \frac{R}{100}\right)^T - P \]
Given Information
- Rate of interest (R) = 5%
- Time (T) = 2 years
- Difference between CI and SI = Rs. 15
Calculating Simple Interest (SI)
For 2 years:
\[ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]
Calculating Compound Interest (CI)
For 2 years:
\[ CI = P \left(1 + \frac{5}{100}\right)^2 - P \]
\[ CI = P \left(1.05^2\right) - P = P \left(1.1025 - 1\right) = 0.1025P \]
Finding the Difference
Now, we can find the difference:
\[ CI - SI = 0.1025P - \frac{P}{10} = 15 \]
Convert \(\frac{P}{10}\) to a decimal:
\[ 0.1025P - 0.1P = 15 \]
\[ 0.0025P = 15 \]
\[ P = \frac{15}{0.0025} = 6000 \]
Conclusion
The sum of money deposited is Rs. 6,000, which corresponds to option 'A'.
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The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer?
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The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer?.
The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer?.
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