Nikita invests Rs 6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs 6.720. Calculate :
the amount at the end of the second year.

Answer

To solve the problem step by step, we need to calculate the amount at the end of the second year after Nikita invests Rs 6,000 for two years at a certain rate of interest compounded annually.

### Step 1: Calculate the interest earned in the first year
- **Given:**
- Principal (P) = Rs 6,000
- Amount after 1 year (A1) = Rs 6,720

- **Interest (I) for the first year can be calculated as:**
\[ I = A1 - P = 6720 - 6000 = 720 \text{ Rs} \]

### Step 2: Calculate the rate of interest (R)
- **Using the formula for simple interest:**
\[ I = \frac{P \times R \times T}{100} \]
where \( T = 1 \) year.

- **Substituting the known values:**
\[ 720 = \frac{6000 \times R \times 1}{100} \]

- **Rearranging to find R:**
\[ R = \frac{720 \times 100}{6000} = 12\% \]

### Step 3: Calculate the amount at the end of the second year
- **Using the compound interest formula:**
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where \( P = 6000 \), \( R = 12\% \), and \( T = 2 \) years.

- **Substituting the values:**
\[ A = 6000 \left(1 + \frac{12}{100}\right)^2 \]
\[ A = 6000 \left(1 + 0.12\right)^2 \]
\[ A = 6000 \left(1.12\right)^2 \]
\[ A = 6000 \times 1.2544 = 7526.4 \text{ Rs} \]

### Final Answer:
The amount at the end of the second year is Rs 7,526.4.

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