Question

A man deposits Rupees \(5000\) in Bank ‘A' at the simple interest rate of \(5\%\) per annum. On the same day, he deposits same amount in another Bank ‘B' at the compound interest rate of \(5\%\) per annum. What amounts will he receive from the two banks on maturity, after three years?

• A. \(15750\) and \(15788\) respectively
• B. \(5750\) and \(6750\) respectively
• C. \(5750\) and \(5788\) respectively
• D. \(5788\) and \(6788\) respectively

Hint:

For simple interest, use \(A=P+\frac{PRT}{100}\). For compound interest, use \(A=P\left(1+\frac{R}{100}\right)^T\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to compute the total accumulated amounts after 3 years for simple interest (Bank A) and compound interest (Bank B) with a principal of Rs 5000 and a rate of 5%.

Step 2: Key Formula or Approach:

• Simple Interest (SI) Amount: \[ A_{\text{SI}} = P + \text{SI} = P + \frac{P \times R \times T}{100} \]
• Compound Interest (CI) Amount: \[ A_{\text{CI}} = P \left(1 + \frac{R}{100}\right)^T \] where $P = 5000$, $R = 5\%$, and $T = 3$ years.

Step 3: Detailed Explanation:

• Bank A (Simple Interest Amount):
\[ A_{\text{SI}} = 5000 + \frac{5000 \times 5 \times 3}{100} \] \[ A_{\text{SI}} = 5000 + 750 = 5750 \text{ rupees} \]
• Bank B (Compound Interest Amount):
\[ A_{\text{CI}} = 5000 \left(1 + \frac{5}{100}\right)^3 \] \[ A_{\text{CI}} = 5000 \times (1.05)^3 \] \[ A_{\text{CI}} = 5000 \times 1.157625 = 5788.125 \approx 5788 \text{ rupees} \]

Step 4: Final Answer:
The amounts are Rs 5750 and Rs 5788 respectively, which matches Option (C).