Question

To start a KFC outlet, Shami borrowed Rs.80,000 at 10% p.a. simple interest. He immediately invested this money at 10% p.a., the interest compound half yearly. Calculate shami's profit in 18 months.

 

1.

Rs. 610

2. Rs. 720
3. Rs. 510
4. Rs. 420

Answer 1

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