Correct Answer - Option 1 :

Rs. 610

**Given∶ **

Principal Rs.80,000 ,Rate = 10% p.a., Time = 18 months= 18/12 years, 3/2 years

**Formula** **Used**∶

S.I = PRT/100

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

C.I = A - P

**Calculation∶**

Here, Principal = Rs. 80,000

Rate = 10% p.a.

Time = 18 months = 18/12 years = 3/2 years

Simple interest paid by Shami in 18 months ∶

S.I = PRT/100 = 80,000 × 10 × 3/100 × 2 = Rs.12,000

Compound interest earned by Shami in 18 months ∶

As, the interest is compounded half yearly, so

Rate will become half & time will be double

R = 10/2 = 5%

T = n = (3/2) × 2 = 3

A = P (1 + R/100)^{n} = 80000 (1 + 5/100)^{3}

⇒ 80000(21/20)^{3}

⇒ Rs. 92610

C.I. earned by Shami in 18 months = A - P = 92610 - 80000

⇒ Rs. 12610

Shami's gain in 18 months = C.I. earned - S.I. paid = 12610 - 12000

⇒ Rs 610.

∴ the correct answer is Rs.610