A sum of Rs. 5324/- is accumulated in 3 years at 10% compound interest. What is the original amount.

Options

A. Rs 2000
B. Rs 4000
C. Rs 6000
D. Rs 3000

Answer

To find the original amount (principal) that accumulates to Rs. 5324 in 3 years at a compound interest rate of 10%, we can use the formula for compound interest:

### Step-by-step Solution:

1. **Identify the variables:**
- Amount (A) = Rs. 5324
- Rate of interest (r) = 10%
- Time (t) = 3 years
- Principal (P) = ?

2. **Use the compound interest formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Substituting the known values into the formula:
\[ 5324 = P \left(1 + \frac{10}{100}\right)^3 \]

3. **Simplify the equation:**
\[ 5324 = P \left(1 + 0.10\right)^3 \]
\[ 5324 = P \left(1.10\right)^3 \]

4. **Calculate \( (1.10)^3 \):**
\[ (1.10)^3 = 1.331 \]
So, we can rewrite the equation as:
\[ 5324 = P \times 1.331 \]

5. **Solve for P (Principal):**
\[ P = \frac{5324}{1.331} \]
Now, calculating the value:
\[ P \approx 4000 \]

### Conclusion:
The original amount (principal) is Rs. 4000.

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