A person invested Rs.5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given` (1.1)^4 = 1.4641` ]

Answer

To find the amount accumulated after 4 years when a person invests Rs. 5,000 every year at an interest rate of 10% compounded annually, we can use the formula for the future value of an ordinary annuity:

\[ A = C \times \frac{(1 + i)^n - 1}{i} \]

Where:
- \( A \) = the total amount accumulated after \( n \) years
- \( C \) = the annual investment (cash flow)
- \( i \) = the annual interest rate (as a decimal)
- \( n \) = the number of years

### Step-by-Step Solution:

1. **Identify the variables**:
- Annual investment \( C = 5000 \)
- Annual interest rate \( r = 10\% = 0.1 \)
- Number of years \( n = 4 \)

2. **Calculate \( 1 + i \)**:
\[ 1 + i = 1 + 0.1 = 1.1 \]

3. **Calculate \( (1 + i)^n \)**:
\[ (1 + i)^n = (1.1)^4 \]
Given that \( (1.1)^4 = 1.4641 \).

4. **Substitute values into the formula**:
\[ A = 5000 \times \frac{(1.4641 - 1)}{0.1} \]

5. **Calculate \( (1.4641 - 1) \)**:
\[ 1.4641 - 1 = 0.4641 \]

6. **Substitute this back into the formula**:
\[ A = 5000 \times \frac{0.4641}{0.1} \]

7. **Calculate \( \frac{0.4641}{0.1} \)**:
\[ \frac{0.4641}{0.1} = 4.641 \]

8. **Final calculation**:
\[ A = 5000 \times 4.641 = 23205 \]

Thus, the amount accumulated after 4 years is **Rs. 23,205**.