Ms Aniket finds that there is `80%` increase in an amount in 8 years at simple interest. What shall be the compunded interest of Rs.14,000 after 3 years at the same rate?

Options

A. Rs.3,794
B. Rs.3,714
C. Rs.4,612
D. Rs.4,634

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Understand the Problem
Ms. Aniket finds that there is an 80% increase in an amount in 8 years at simple interest. We need to find the compound interest on Rs. 14,000 after 3 years at the same rate.

### Step 2: Calculate the Rate of Interest
1. **Let the Principal Amount (P)** = Rs. 100 (for simplicity).
2. **Increase in Amount** = 80% of Rs. 100 = Rs. 80.
3. **Simple Interest (SI)** = Rs. 80.
4. **Time (T)** = 8 years.

Using the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI = 80 \)
- \( P = 100 \)
- \( T = 8 \)

Plugging in the values:
\[ 80 = \frac{100 \times R \times 8}{100} \]
\[ 80 = 8R \]
\[ R = \frac{80}{8} = 10\% \]

### Step 3: Calculate the Compound Interest for Rs. 14,000
1. **Principal Amount (P)** = Rs. 14,000.
2. **Rate (R)** = 10% (from previous calculation).
3. **Time (T)** = 3 years.

Using the formula for Compound Interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P = 14,000 \)
- \( R = 10 \)
- \( T = 3 \)

Plugging in the values:
\[ A = 14000 \left(1 + \frac{10}{100}\right)^3 \]
\[ A = 14000 \left(1 + 0.1\right)^3 \]
\[ A = 14000 \left(1.1\right)^3 \]

### Step 4: Calculate \( (1.1)^3 \)
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 5: Calculate the Amount
Now substituting back:
\[ A = 14000 \times 1.331 \]
\[ A = 18634 \]

### Step 6: Calculate the Compound Interest
Now, we calculate the Compound Interest (CI):
\[ CI = A - P \]
\[ CI = 18634 - 14000 \]
\[ CI = 4634 \]

### Final Answer
The compound interest on Rs. 14,000 after 3 years at the same rate is **Rs. 4,634**.

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