Calculate the amount and the compound interest on:
(i) रु 6,000 in 3 years at 5% per year.
(ii) रु 8,000 in 2 years at 15% per annum.

Explanation

To solve the question of calculating the amount and compound interest for the given scenarios, we will use the formula for compound interest:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Part (i): Calculate for रु 6,000 in 3 years at 5% per annum.

1. **Identify the values:**
- Principal \( P = 6000 \)
- Rate \( R = 5\% \)
- Time \( T = 3 \) years

2. **Substitute the values into the formula:**
\[ A = 6000 \left(1 + \frac{5}{100}\right)^3 \]

3. **Calculate \( \frac{5}{100} \):**
\[ \frac{5}{100} = 0.05 \]

4. **Add 1 to \( 0.05 \):**
\[ 1 + 0.05 = 1.05 \]

5. **Raise \( 1.05 \) to the power of 3:**
\[ 1.05^3 = 1.157625 \]

6. **Multiply by the principal:**
\[ A = 6000 \times 1.157625 = 6945.75 \]

7. **Calculate the compound interest (CI):**
\[ CI = A - P = 6945.75 - 6000 = 945.75 \]

### Summary for Part (i):
- Amount after 3 years: रु 6945.75
- Compound Interest: रु 945.75

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### Part (ii): Calculate for रु 8,000 in 2 years at 15% per annum.

1. **Identify the values:**
- Principal \( P = 8000 \)
- Rate \( R = 15\% \)
- Time \( T = 2 \) years

2. **Substitute the values into the formula:**
\[ A = 8000 \left(1 + \frac{15}{100}\right)^2 \]

3. **Calculate \( \frac{15}{100} \):**
\[ \frac{15}{100} = 0.15 \]

4. **Add 1 to \( 0.15 \):**
\[ 1 + 0.15 = 1.15 \]

5. **Raise \( 1.15 \) to the power of 2:**
\[ 1.15^2 = 1.3225 \]

6. **Multiply by the principal:**
\[ A = 8000 \times 1.3225 = 10580 \]

7. **Calculate the compound interest (CI):**
\[ CI = A - P = 10580 - 8000 = 2580 \]

### Summary for Part (ii):
- Amount after 2 years: रु 10,580
- Compound Interest: रु 2,580

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