Option 3 : Rs. 205

**Given:**

Sum = Rs. 2000

Time = 1 year

Rate = 10%

Concept used:

When the sum is compounded half-yearly, then the rate of interest becomes half and time becomes double.

**Formula used:**

A = P (1 + R/100)T

C.I = A - P

Where, A = Amount, P = Principal, T = Time, C.I = Compound interest and R = rate of interest

**Calculation:**

According to the question,

R = 10%/2 = 5%

T = 2 × 1 = 2 years

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

⇒ 2000(1 + 5/100)^{2}

⇒ 2000(1 + 1/20)^{2}

⇒ 2000(21/20)2

⇒ 2000(441/400)

⇒ 5 × 441

⇒ 2205

C.I = 2205 - 2000

⇒ 205

**∴ The compound interest is Rs. 205.**

We'll use successive percentage method to solve this

Total percentage change = [a + b + (ab)/100]%, where a and b are positive percentage change

Here rate will be 10/2 = 5% (As compounded half yearly)

Total interest for 1 year compounded half yearly = [5 + 5 + (5 × 5)/100]** % **

⇒ Total interest = 10.25%

Compound interest = 10.25% of 2000 = 205

∴ The compound interest is Rs. 205.