# 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.

1.  Rs. 840
2. Rs. 932
3. Rs. 520
4. Rs. 640
Monis Rasool Professor Asked on 12th September 2015 in

Answer: (4) Rs. 640

Explanation:-
Let the principal be Rs. X.
Given-
Rate = 5%, Time = 2 years and the difference between C I and 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.

Anurag Mishra Professor Answered on 13th September 2015.