Radha deposit a certain sum of money every year at 8% C.I. After 3 years Rs. 54783 was in her account. Find the sum of money which she deposit in her account every year.

Answer

To solve the problem, we will use the formula for the compound interest and the concept of future value.

### Step-by-Step Solution:

1. **Understanding the Problem**:
Radha deposits a certain sum of money (let's call it \( P \)) every year at an interest rate of 8% compounded annually. After 3 years, the total amount in her account is Rs. 54783.

2. **Future Value of Annuity Formula**:
The future value \( A \) of an annuity (regular deposits) can be calculated using the formula:
\[ A = P \times \frac{(1 + r)^n - 1}{r} \]
where:
- \( A \) = total amount after \( n \) years
- \( P \) = annual deposit
- \( r \) = annual interest rate (as a decimal)
- \( n \) = number of years

3. **Substituting Known Values**:
Here, \( A = 54783 \), \( r = 0.08 \), and \( n = 3 \).
Substituting these values into the formula gives:
\[ 54783 = P \times \frac{(1 + 0.08)^3 - 1}{0.08} \]

4. **Calculating the Factor**:
First, calculate \( (1 + 0.08)^3 \):
\[ (1.08)^3 = 1.259712 \]
Now, calculate \( (1.259712 - 1) \):
\[ 1.259712 - 1 = 0.259712 \]
Now, divide by \( 0.08 \):
\[ \frac{0.259712}{0.08} = 3.2464 \]

5. **Setting Up the Equation**:
Now we have:
\[ 54783 = P \times 3.2464 \]

6. **Solving for \( P \)**:
To find \( P \), divide both sides by \( 3.2464 \):
\[ P = \frac{54783}{3.2464} \approx 16800 \]

### Final Answer:
The sum of money which Radha deposits in her account every year is approximately Rs. 16800.