# Find the Simple Interest:

If the difference between the compound interest and simple interest on a sum of money at 5% per annum for 2 year is Rs 16. Find the simple interest.

- Rs. 840
- Rs. 932
- Rs. 520
- Rs. 640

**Answer: (4) Rs. 640**

Explanation:-

**Let the principal be Rs. X.**

Given-

**Rate = 5%, Time = 2 years and the difference between C I a****nd S I = Rs. 16**

**Formula-**

**Simple Interest = P x R x T/100**

**Where, P = principal, R = rate, & T = time.**

**Formula-**

**Compound Interest = P [(1 + R/100)**^{t}** ****– 1]**

**Where, P = principal, R = rate, t = time.**

According to the question,

**Formula-**

**Compound Interest = P [(1 + R/100)**^{t}** ****– 1]**

**Where, P = principal, R = rate, t = time.**

According to the question,

X[(1 + 5/100)^{2} – 1] – X x 5 x 2/100 = 16

X[(21/20)^{2} – 1 ] – X/10 = 16

X[441/400 – 1] – X/10 = 16

X[441 – 400]/400 – X/10 = 16

X (41 – 40)/400 = 16

X/400 = 16

X = 16 x 400

X = Rs. 6400

Then, Simple interest = 6400 x 5 x 2/100

= 64 x 5 x 2

= Rs. 640

Then, the simple interest is Rs. 640.

Hence, the answer is (4) Rs. 640.