The sum that amounts to Rs 4913 in 3 years at `6(1)/(4)%` per annum compounded annually. Is

Options

A. Rs 3096
B. Rs 4076
C. Rs 4085
D. Rs 4096

Answer

To find the principal amount that amounts to Rs. 4913 in 3 years at a rate of 6.25% per annum compounded annually, we will use the formula for compound interest.

### Step-by-Step Solution:

1. **Identify the given values:**
- Amount (A) = Rs. 4913
- Time (n) = 3 years
- Rate (R) = 6.25% per annum

2. **Convert the rate from mixed fraction to improper fraction:**
- 6.25% can be expressed as \( \frac{25}{4} \% \).

3. **Write the formula for compound interest:**
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- A = Amount
- P = Principal
- R = Rate of interest
- n = Time in years

4. **Substitute the known values into the formula:**
\[ 4913 = P \left(1 + \frac{25/4}{100}\right)^3 \]

5. **Simplify the expression inside the bracket:**
- First, convert \( \frac{25}{4} \) to a decimal:
\[ \frac{25}{4} = 6.25 \]
- Now, convert this to a fraction of 100:
\[ \frac{25/4}{100} = \frac{25}{400} = \frac{1}{16} \]
- Therefore, we have:
\[ 1 + \frac{1}{16} = \frac{16 + 1}{16} = \frac{17}{16} \]

6. **Substitute back into the equation:**
\[ 4913 = P \left(\frac{17}{16}\right)^3 \]

7. **Calculate \( \left(\frac{17}{16}\right)^3 \):**
\[ \left(\frac{17}{16}\right)^3 = \frac{17^3}{16^3} = \frac{4913}{4096} \]

8. **Rearranging the equation to find P:**
\[ P = 4913 \times \frac{16^3}{17^3} \]

9. **Calculate \( 16^3 \) and \( 17^3 \):**
- \( 16^3 = 4096 \)
- \( 17^3 = 4913 \)

10. **Substituting back:**
\[ P = 4913 \times \frac{4096}{4913} \]
- The \( 4913 \) cancels out:
\[ P = 4096 \]

### Final Answer:
The principal amount is Rs. 4096.

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