On a certain sum of m

Question

On a certain sum of money, the simple interest for 2 years is Rs. 200 at the rate of 7% per annum. Find the difference in C.I. and S.I.

Options:

A . None of these

B . Rs. 9

C . Rs. 7

D . Rs. 11

Answer: Option C

Answer : Option C

Explanation :

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Solution 1
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Simple Interest for 2 years = Rs.200
$MF#%\text{Sum, P} = \dfrac{100 \times \text{SI}}{\text{RT}} = \dfrac{100 \times 200}{7 \times 2} = \dfrac{100 \times 100}{7}\\\\ \text{Compound Interest = }\text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} - \text{P}\\\\ = \text{P}\left(1 + \dfrac{7}{100}\right)^2 - \text{P} = \text{P}\left[\left(1 + \dfrac{7}{100}\right)^2 - 1\right] = \text{P}\left(1 + \dfrac{14}{100} + \dfrac{49}{10000} - 1\right)=\text{P}\left(\dfrac{14}{100} + \dfrac{49}{10000}\right) \\\\= \dfrac{100 \times 100}{7}\left(\dfrac{14}{100} + \dfrac{49}{10000}\right)=200 + 7 = \text{Rs. }207$MF#%
Required Difference = 207 - 200 = Rs.7
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Solution 2
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The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
$MF#% = \dfrac{\text{R} \times \text{SI}}{2 \times 100} $MF#%

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