Find the amount of Rs 12000 after 3 years at the rate of 12% per annum compounded annually.

Answer

To find the amount of Rs 12,000 after 3 years at the rate of 12% per annum compounded annually, we will use the compound interest formula:

### Step-by-Step Solution:

1. **Identify the Variables:**
- Principal (P) = Rs 12,000
- Rate of interest (R) = 12% per annum
- Time (N) = 3 years

2. **Write the Compound Interest Formula:**
The formula for calculating the amount (A) when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]

3. **Substitute the Values into the Formula:**
Plugging in the values we have:
\[ A = 12000 \left(1 + \frac{12}{100}\right)^3 \]

4. **Calculate the Rate Component:**
First, calculate \(1 + \frac{12}{100}\):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

5. **Raise to the Power of N:**
Now, raise \(1.12\) to the power of \(3\):
\[ 1.12^3 = 1.12 \times 1.12 \times 1.12 \]
Calculating this step-by-step:
- \(1.12 \times 1.12 = 1.2544\)
- \(1.2544 \times 1.12 = 1.404928\) (approximately)

6. **Multiply by the Principal:**
Now multiply this result by the principal:
\[ A = 12000 \times 1.404928 \approx 16805.136 \]

7. **Final Amount:**
Therefore, the amount after 3 years is approximately:
\[ A \approx Rs 16805.14 \]

### Final Answer:
The amount after 3 years will be approximately Rs 16805.14.