Question : The difference between Compound Interest and Simple Interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the total sum?
Option 1: Rs. 7,200
Option 2: Rs. 9,600
Option 3: Rs. 16,400
Option 4: Rs. 8,400
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Correct Answer: Rs. 16,400
Solution :
The difference between the Simple Interest and Compound Interest on a certain sum of money $P$ for 2 years at $R$% per annum is given by:
$(CI - SI) = \frac{PR^{2}}{100^{2}}$
According to Question,
The difference between CI and SI for 2 years is 41.
So, $ 41= \frac{P(5)^{2}}{100^{2}}$
⇒ $P = \frac{41\times100\times100}{5\times5}$
⇒ $P = 16400$
Hence, the correct answer is Rs. 16,400.
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