# The compound interest on a certain sum at 16 2/3 % per annum for 3 years is 12,700

The compound interest on a certain sum at 16 2/3 % per annum for 3 years is 12,700. The simple interest on the same sum with same rate of interest and for the same period is

(1)Rs.9,600

(2) Rs. 10,800

(3) Rs. 12,000

(4) Rs. 10,200

**Answer: (2) Rs.10,800**

**Solution:-**

Let Principal be Rs.X

Rate = 50/3%, Time = 3 years and Compound Interest = Rs.12,700

Then, 12,700 = {X(50/3×100 + 1)^{3} – X}

12,700 = X{(1/6 + 1)^{3} – 1}

12,700 = X (7/6)^{3} – X

12,700 = 343 X/216 – X

12,700 = (343 X – 216 X)/216

12,700 = 127 X/216

X = 216 x 100

X = 21600

Then, Simple Interest of Rs.21,600 = 21,600 x 3 x 50 /3 x 100

= 216 x 50

= 10,800

So, the simple Interest is Rs.10,800.

Hence, the correct answer is option (2) Rs.10,800.