The difference in the simple interest offered by banks on ₹5000 for two years is ₹25. State the difference between the interest rates of both banks.
Understand the Problem
The question is asking for the calculation of the difference in interest rates between two banks based on the difference in simple interest earned on ₹5000 over two years, which amounts to ₹25. The user needs assistance in finding the rates of interest for both banks.
Answer
The difference between the interest rates of both banks is $0.25\%$.
Answer for screen readers
The difference between the interest rates of both banks is $0.25%$.
Steps to Solve
- Understand the simple interest formula
The formula for simple interest (SI) is given by:
$$ SI = \frac{P \times r \times t}{100} $$
Where:
- ( P ) is the principal amount (₹5000 in this case),
- ( r ) is the rate of interest,
- ( t ) is the time period in years (2 years here).
- Calculate the total interest for both banks
If the difference in interest earned over 2 years is ₹25, we can represent the interest from both banks as:
-
For Bank A: $$ SI_A = \frac{5000 \times r_A \times 2}{100} $$
-
For Bank B: $$ SI_B = \frac{5000 \times r_B \times 2}{100} $$
- Set up the equation for the difference in interest
Given that the difference in interest is ₹25, we can write:
$$ SI_A - SI_B = 25 $$
Substituting in the equations:
$$ \left(\frac{5000 \times r_A \times 2}{100}\right) - \left(\frac{5000 \times r_B \times 2}{100}\right) = 25 $$
- Simplify the equation
Factoring out common terms:
$$ 100 \left(\frac{5000 \times 2}{100}\right) (r_A - r_B) = 25 $$
This simplifies to:
$$ 100 \cdot 100 (r_A - r_B) = 25 $$
- Solve for the difference in rates
Simplifying further, we can find ( r_A - r_B ):
$$ 100(r_A - r_B) = \frac{25}{100} $$
$$ r_A - r_B = \frac{25}{10000} $$
$$ r_A - r_B = 0.0025 $$
Thus the difference in the interest rates of both banks (in percentage) is:
$$ r_A - r_B = 0.25% $$
The difference between the interest rates of both banks is $0.25%$.
More Information
The interest calculation involves understanding how simple interest works. A small difference in interest can still represent a measurable change in returns over time. This problem illustrates how small percentages can have a tangible effect, particularly when dealing with larger principal amounts.
Tips
- Confusing the units of interest (percent vs. actual amount).
- Not correctly simplifying the equation leading to erroneous conclusions.
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