Correct Answer - Option 2 :

\(1 \frac{1}{2}\) years

**Given:**

Principal = Rs. 800

Rate = 10% per annum compounded semi-annually

Amount = Rs. 926.10

**Formula Used:**

A = P (1 + R/100)^{n}

Where, A = Amount, P = Principal, R = Rate, n = time

**Concept Used:**

When the rate is compounded semi/half annually then

The rate becomes R/2 and Time becomes 2n

**Calculation:**

Let the required time be n

According to the question

Rate (R) = 10/2% = 5%, Time (n) = 2 × n = 2n

Now, We have to find the amount

926.10 = 800 (1 + 5/100)^{2n}

⇒ 926.10/800 = (1 + 5/100)2n

⇒ 1.157625 = (1.05)^{2n}

⇒ (1.05)^{3} = (1.05)2n

⇒ 2n = 3

⇒ n = 3/2 = \(1 \frac{1}{2}\)

**∴ The required time is \(1 \frac{1}{2}\).**