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The compound interest on a certain sum for 2 years at 10% per annum is Rs 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
- a)Rs 400
- b)Rs 500
- c)Rs 600
- d)Rs 800
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The compound interest on a certain sum for 2 years at 10% per annum is...
Let the sum be Rs P.
Then, [P (1 + 10/100)2 – P] = 525
P = (11/10)2 – 1 = 525
P = (525 × 100)/21 = 2500
Therefore, sum = Rs 2500
S.I. = (2500 × 5 × 4)/100 = Rs 500
Then, [P (1 + 10/100)2 – P] = 525
P = (11/10)2 – 1 = 525
P = (525 × 100)/21 = 2500
Therefore, sum = Rs 2500
S.I. = (2500 × 5 × 4)/100 = Rs 500
Most Upvoted Answer
The compound interest on a certain sum for 2 years at 10% per annum is...
Understanding Compound Interest
To find the principal amount (P) using the compound interest formula, we start with the information given:
- **Compound Interest (CI)** for 2 years = Rs 525
- **Rate of Interest (R)** = 10% per annum
- **Time (T)** = 2 years
The formula for compound interest is:
\[ CI = P \times \left( \left(1 + \frac{R}{100}\right)^T - 1 \right) \]
Substituting the values:
\[ 525 = P \times \left( \left(1 + \frac{10}{100}\right)^2 - 1 \right) \]
Calculating:
\[ \left(1 + 0.1\right)^2 = 1.21 \]
So:
\[ 525 = P \times (1.21 - 1) \]
\[ 525 = P \times 0.21 \]
Now, solving for P:
\[ P = \frac{525}{0.21} = 2500 \]
Calculating Simple Interest
Now that we have the principal amount (P = Rs 2500), we can calculate the simple interest for double the time at half the rate.
- **New Time (T)** = 4 years (double the time)
- **New Rate (R)** = 5% per annum (half of 10%)
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{2500 \times 5 \times 4}{100} \]
Calculating:
\[ SI = \frac{50000}{100} = 500 \]
Final Answer
The simple interest on the sum for double the time at half the rate per annum is Rs 500. Thus, the correct answer is option 'B'.
To find the principal amount (P) using the compound interest formula, we start with the information given:
- **Compound Interest (CI)** for 2 years = Rs 525
- **Rate of Interest (R)** = 10% per annum
- **Time (T)** = 2 years
The formula for compound interest is:
\[ CI = P \times \left( \left(1 + \frac{R}{100}\right)^T - 1 \right) \]
Substituting the values:
\[ 525 = P \times \left( \left(1 + \frac{10}{100}\right)^2 - 1 \right) \]
Calculating:
\[ \left(1 + 0.1\right)^2 = 1.21 \]
So:
\[ 525 = P \times (1.21 - 1) \]
\[ 525 = P \times 0.21 \]
Now, solving for P:
\[ P = \frac{525}{0.21} = 2500 \]
Calculating Simple Interest
Now that we have the principal amount (P = Rs 2500), we can calculate the simple interest for double the time at half the rate.
- **New Time (T)** = 4 years (double the time)
- **New Rate (R)** = 5% per annum (half of 10%)
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{2500 \times 5 \times 4}{100} \]
Calculating:
\[ SI = \frac{50000}{100} = 500 \]
Final Answer
The simple interest on the sum for double the time at half the rate per annum is Rs 500. Thus, the correct answer is option 'B'.
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The compound interest on a certain sum for 2 years at 10% per annum is Rs 525. The simple interest on the same sum for double the time at half the rate percent per annum is:a)Rs 400b)Rs 500c)Rs 600d)Rs 800Correct answer is option 'B'. Can you explain this answer?
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The compound interest on a certain sum for 2 years at 10% per annum is Rs 525. The simple interest on the same sum for double the time at half the rate percent per annum is:a)Rs 400b)Rs 500c)Rs 600d)Rs 800Correct answer is option 'B'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The compound interest on a certain sum for 2 years at 10% per annum is Rs 525. The simple interest on the same sum for double the time at half the rate percent per annum is:a)Rs 400b)Rs 500c)Rs 600d)Rs 800Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a certain sum for 2 years at 10% per annum is Rs 525. The simple interest on the same sum for double the time at half the rate percent per annum is:a)Rs 400b)Rs 500c)Rs 600d)Rs 800Correct answer is option 'B'. Can you explain this answer?.
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