A sum of ₹50000 was invested in scheme A at `12%` per annum simple interest for three years. A sum of ₹40000 was invested in scheme B at `10%` per annum compound interest compounded annually for 2 years. What is the difference between final amount received from scheme A and that received from scheme B

Options

A. ₹19600
B. ₹20200
C. ₹19000
D. ₹19200

Answer

To solve the problem, we need to calculate the final amounts received from both Scheme A and Scheme B, and then find the difference between these amounts.

### Step-by-Step Solution:

**Step 1: Calculate Simple Interest for Scheme A**
- The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]
- For Scheme A:
- Principal (P) = ₹50,000
- Rate (R) = 12%
- Time (T) = 3 years
- Plugging in the values:
\[ \text{SI} = \frac{50000 \times 12 \times 3}{100} = \frac{1800000}{100} = ₹18000 \]

**Step 2: Calculate Total Amount for Scheme A**
- The total amount (A) received from Scheme A is:
\[ A = \text{Principal} + \text{Simple Interest} = 50000 + 18000 = ₹68000 \]

**Step 3: Calculate Compound Interest for Scheme B**
- The formula for Compound Interest (CI) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
- For Scheme B:
- Principal (P) = ₹40,000
- Rate (R) = 10%
- Time (T) = 2 years
- Plugging in the values:
\[ A = 40000 \left(1 + \frac{10}{100}\right)^2 = 40000 \left(1 + 0.1\right)^2 = 40000 \left(1.1\right)^2 \]
\[ A = 40000 \times 1.21 = ₹48400 \]

**Step 4: Calculate the Difference Between the Two Amounts**
- The difference between the amounts received from Scheme A and Scheme B is:
\[ \text{Difference} = A_{\text{Scheme A}} - A_{\text{Scheme B}} = 68000 - 48400 = ₹19600 \]

### Final Answer:
The difference between the final amount received from Scheme A and that received from Scheme B is **₹19600**.

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