Mohit invests रु 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to रु 9,440. Calculate
(i) the rate of interest per annum.
(ii) the amount at the end of the second year.
(iii) the interest accrued in the third year.

Explanation

To solve the problem step by step, we will follow the instructions provided in the question.

### Given:
- Principal (P) = रु 8,000
- Amount after 1 year (A1) = रु 9,440
- Time (T) = 1 year

### (i) Calculate the rate of interest per annum.

1. **Calculate the Simple Interest (SI) for the first year:**
\[ SI = A1 - P = 9,440 - 8,000 = 1,440 \text{ rupees} \]

2. **Use the formula for Simple Interest:**
\[ SI = \frac{P \times R \times T}{100} \]
Here, we know SI = 1,440, P = 8,000, and T = 1 year. We need to find R (rate of interest).

3. **Substituting the values into the formula:**
\[ 1,440 = \frac{8,000 \times R \times 1}{100} \]

4. **Rearranging to solve for R:**
\[ R = \frac{1,440 \times 100}{8,000} \]

5. **Calculating R:**
\[ R = \frac{144,000}{8,000} = 18\% \]

### (ii) Calculate the amount at the end of the second year.

1. **Using the formula for compound interest:**
\[ A2 = P \left(1 + \frac{R}{100}\right)^T \]
Here, P = 8,000, R = 18%, and T = 2 years.

2. **Substituting the values:**
\[ A2 = 8,000 \left(1 + \frac{18}{100}\right)^2 \]

3. **Calculating inside the parentheses:**
\[ A2 = 8,000 \left(1 + 0.18\right)^2 = 8,000 \left(1.18\right)^2 \]

4. **Calculating \( (1.18)^2 \):**
\[ (1.18)^2 = 1.3924 \]

5. **Calculating A2:**
\[ A2 = 8,000 \times 1.3924 = 11,139.20 \text{ rupees} \]

### (iii) Calculate the interest accrued in the third year.

1. **Calculate the amount at the end of the third year (A3):**
\[ A3 = P \left(1 + \frac{R}{100}\right)^3 \]
Here, P = 8,000, R = 18%, and T = 3 years.

2. **Substituting the values:**
\[ A3 = 8,000 \left(1 + \frac{18}{100}\right)^3 = 8,000 \left(1.18\right)^3 \]

3. **Calculating \( (1.18)^3 \):**
\[ (1.18)^3 \approx 1.5927 \]

4. **Calculating A3:**
\[ A3 = 8,000 \times 1.5927 \approx 12,741.60 \text{ rupees} \]

5. **Calculate the interest accrued in the third year (I3):**
\[ I3 = A3 - A2 = 12,741.60 - 11,139.20 = 1,602.40 \text{ rupees} \]

### Final Answers:
(i) Rate of interest per annum = **18%**
(ii) Amount at the end of the second year = **11,139.20 rupees**
(iii) Interest accrued in the third year = **1,602.40 rupees**