Question

Rs. 160000 is divided into two equal parts. One part is invested in a scheme giving \(12%\) interest compounded annually for \(2\) years. The other part is invested in a scheme offering simple interest of \(13%\) for \(2\) years. Find the difference between the interest earned in the two schemes. 
 

• A. 512
• B. 426
• C. 448
• D. 568

Hint:

For compound interest, remember to apply the rate successively for each year. For simple interest, the formula is straightforward: \( \frac{P \times R \times T}{100} \).

Answer 1

The Correct Option is A

Solution:
Step 1 (Divide the amount into two parts).
Total amount = \(\rupee 160000\), so each part = \(\frac{160000}{2} = \rupee 80000\). Step 2 (Interest from compound interest scheme).
Rate \(R = 12%\) p.a., time \(n=2\) years, principal \(P = 80000\). Amount after 2 years: \[ A = P(1 + \frac{R}{100})^n = 80000 \left(1 + \frac{12}{100}\right)^2 = 80000 \times (1.12)^2 \] \[ = 80000 \times 1.2544 = \rupee 100352 \] Compound interest = \(100352 - 80000 = \rupee 20352\). Step 3 (Interest from simple interest scheme).
Rate \(= 13%\) p.a., time \(t = 2\) years, principal \(= 80000\): \[ \text{SI} = \frac{P \times R \times t}{100} = \frac{80000 \times 13 \times 2}{100} = \rupee 20800. \] Step 4 (Difference in interest).
\[ \text{Difference} = 20800 - 20352 = \rupee 448 \] \(\) This matches option C, not A — so correct answer should be \(\rupee 448\). \[ {\rupee 448 \ \text{(Option (c)}} \]