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

For Bank A, simple interest is applied. Principal is: \[ P=5000. \] Rate is: \[ R=5\%. \] Time is: \[ T=3\text{ years}. \] Simple interest is: \[ SI=\frac{PRT}{100}. \] Substitute the values: \[ SI=\frac{5000\times5\times3}{100}. \] \[ SI=750. \] Amount from Bank A is: \[ A=P+SI. \] \[ A=5000+750. \] \[ A=5750. \] Now for Bank B, compound interest is applied. Compound amount is: \[ A=P\left(1+\frac{R}{100}\right)^T. \] \[ A=5000\left(1+\frac{5}{100}\right)^3. \] \[ A=5000(1.05)^3. \] \[ A=5000(1.157625). \] \[ A=5788.125. \] Approximately: \[ A=5788. \] Therefore, the amounts received are: \[ 5750\text{ and }5788. \]