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The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?
  • a)
    200/7 
  • b)
    100/7 
  • c)
    300/7 
  • d)
    400/7 
Correct answer is option 'A'. Can you explain this answer?
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Understanding Interest Types
To solve this problem, we first need to understand the difference between compound interest (CI) and simple interest (SI).
- Simple Interest Formula: SI = P * r * t
- Compound Interest Formula: CI = P * (1 + r)^t - P
Where:
- P = Principal amount
- r = Rate of interest per annum (as a decimal)
- t = Time in years
Difference Between CI and SI
The difference between compound interest and simple interest for a certain period can be calculated as follows:
- For 2 years: Difference (D2) = CI (2 years) - SI (2 years)
- For 3 years: Difference (D3) = CI (3 years) - SI (3 years)
Given the ratio of these differences is 23:7, we can express this mathematically:
- D3 / D2 = 23 / 7
Calculating Differences
Using the formulas:
1. For 2 years:
- D2 = P * (r^2) / 100^2
2. For 3 years:
- D3 = P * (r^3) / 100^3
Now substituting D2 and D3 into the ratio:
- (P * (r^3) / 100^3) / (P * (r^2) / 100^2) = 23 / 7
This simplifies to:
- r / 100 = 23 / 7
Finding Rate of Interest
From the above equation, we can derive the rate:
- r = (23 * 100) / 7
Calculating gives:
- r = 2300 / 7
Thus, the rate of interest per annum is:
- Rate = 200 / 7%
Conclusion
The correct answer is option 'A', which is 200/7%.
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The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer?
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