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The difference between the simple and compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?
- a)Rs. 5000
- b)Rs. 6000
- c)Rs. 6250
- d)Rs. 7500
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The difference between the simple and compound interest on a certain s...
Suppose the sum = Rs. P;
Difference of CI and SI for two years = Interest on SI of 1st year
⇒ 10 = (SI of 1st yea × 4 × 1)/100
⇒ SI of 1st year = Rs. 250
∴ 250 = (P × 4 × 1)/100
⇒ P = 25000/4
⇒ P = Rs. 6250
∴ Sum of money = Rs. 6250
Difference of CI and SI for two years = Interest on SI of 1st year
⇒ 10 = (SI of 1st yea × 4 × 1)/100
⇒ SI of 1st year = Rs. 250
∴ 250 = (P × 4 × 1)/100
⇒ P = 25000/4
⇒ P = Rs. 6250
∴ Sum of money = Rs. 6250
Most Upvoted Answer
The difference between the simple and compound interest on a certain s...
Understanding Simple and Compound Interest
To find the sum of money based on the difference between simple and compound interest, we use the following formulas:
- Simple Interest (SI):
\[
\text{SI} = \frac{P \times r \times t}{100}
\]
- Compound Interest (CI):
\[
\text{CI} = P \left(1 + \frac{r}{100}\right)^t - P
\]
Where:
- \( P \) = Principal amount (sum of money)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years
Given Information
- Rate \( r = 4\% \)
- Time \( t = 2 \) years
- Difference between CI and SI = Rs. 10
Calculating Simple Interest
- For 2 years:
\[
\text{SI} = \frac{P \times 4 \times 2}{100} = \frac{8P}{100} = \frac{P}{12.5}
\]
Calculating Compound Interest
- For 2 years:
\[
\text{CI} = P \left(1 + \frac{4}{100}\right)^2 - P = P \left(1.04^2\right) - P = P(1.0816) - P = 0.0816P
\]
Finding the Difference
- The difference between CI and SI is:
\[
\text{Difference} = \text{CI} - \text{SI} = 0.0816P - \frac{P}{12.5}
\]
Setting this equal to Rs. 10:
\[
0.0816P - 0.08P = 10
\]
\[
0.0016P = 10
\]
\[
P = \frac{10}{0.0016} = 6250
\]
Conclusion
The sum of money is Rs. 6250, which corresponds to option 'C'.
To find the sum of money based on the difference between simple and compound interest, we use the following formulas:
- Simple Interest (SI):
\[
\text{SI} = \frac{P \times r \times t}{100}
\]
- Compound Interest (CI):
\[
\text{CI} = P \left(1 + \frac{r}{100}\right)^t - P
\]
Where:
- \( P \) = Principal amount (sum of money)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years
Given Information
- Rate \( r = 4\% \)
- Time \( t = 2 \) years
- Difference between CI and SI = Rs. 10
Calculating Simple Interest
- For 2 years:
\[
\text{SI} = \frac{P \times 4 \times 2}{100} = \frac{8P}{100} = \frac{P}{12.5}
\]
Calculating Compound Interest
- For 2 years:
\[
\text{CI} = P \left(1 + \frac{4}{100}\right)^2 - P = P \left(1.04^2\right) - P = P(1.0816) - P = 0.0816P
\]
Finding the Difference
- The difference between CI and SI is:
\[
\text{Difference} = \text{CI} - \text{SI} = 0.0816P - \frac{P}{12.5}
\]
Setting this equal to Rs. 10:
\[
0.0816P - 0.08P = 10
\]
\[
0.0016P = 10
\]
\[
P = \frac{10}{0.0016} = 6250
\]
Conclusion
The sum of money is Rs. 6250, which corresponds to option 'C'.
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The difference between the simple and compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?a)Rs. 5000b)Rs. 6000c)Rs. 6250d)Rs. 7500Correct answer is option 'C'. Can you explain this answer?
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