There is 60% increase in an amount in 6 years at the rate of simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate ?

Options

A. Rs 2160
B. Rs. 3120
C. Rs. 3972
D. Rs. 6240

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Determine the Rate of Interest
The problem states that there is a 60% increase in an amount in 6 years at the rate of simple interest. This means that the interest earned over 6 years is 60% of the principal amount (P).

Let’s denote:
- Principal (P) = P
- Interest (I) = 60% of P = (60/100) * P = 0.6P
- Time (T) = 6 years

Using the formula for Simple Interest:
\[ I = \frac{P \times R \times T}{100} \]

Substituting the known values:
\[ 0.6P = \frac{P \times R \times 6}{100} \]

### Step 2: Simplify the Equation
We can cancel P from both sides (assuming P ≠ 0):
\[ 0.6 = \frac{R \times 6}{100} \]

Now, rearranging to find R:
\[ R = \frac{0.6 \times 100}{6} \]
\[ R = \frac{60}{6} \]
\[ R = 10\% \]

### Step 3: Calculate Compound Interest for Rs. 12,000
Now that we have the rate of interest (R = 10%), we need to calculate the compound interest for Rs. 12,000 after 3 years.

Using the formula for Compound Interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- A = Amount after time T
- P = Principal = Rs. 12,000
- R = Rate = 10%
- T = Time = 3 years

Substituting the values:
\[ A = 12000 \left(1 + \frac{10}{100}\right)^3 \]
\[ A = 12000 \left(1 + 0.1\right)^3 \]
\[ A = 12000 \left(1.1\right)^3 \]

### 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 Total Amount
Now substituting back into the amount formula:
\[ A = 12000 \times 1.331 \]
\[ A = 15972 \]

### Step 6: Calculate Compound Interest
The compound interest (CI) can be found by subtracting the principal from the total amount:
\[ CI = A - P \]
\[ CI = 15972 - 12000 \]
\[ CI = 3972 \]

### Final Answer
The compound interest of Rs. 12,000 after 3 years at the same rate is **Rs. 3972**.

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