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# If the compound interest on a certain sum for two years at $5\%$ p.a. is Rs$1,100$ the simple interest on it at the same rate for two years will be.(A)Rs. $1250$(B)Rs.$2150$(C)Rs. $2200$(D)Rs. $2300$

Last updated date: 20th Jun 2024
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As per the question we have been given time $(n) = 2$ years, Rate(R) $= 5\%$ and the compound interest is given i.e. $1100$. We have to find simple interests. So first we will calculate the principal.
We know that Compound interest$=$Amount$-$Principal. The formula of Amount is $P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
By substituting the values we get, $1100 = P{\left( {1 + \dfrac{5}{{100}}} \right)^2} - P$. Now we will add the fraction and solve this: $1100 = P{\left( {\dfrac{{105}}{{100}}} \right)^2} - P \Rightarrow 1100 = P{(1.05)^2} - P$. Now we will write the product: $1100 = 1.1025P - P \Rightarrow 1100 = .05P$, By isolating the term P and moving the numbers in right side we have, $P = \dfrac{{1100}}{{0.05}} = \dfrac{{1100 \times 100}}{5}$, It gives us $P = 22000$.
Now we will calculate Simple interest $= \dfrac{{P \times R \times T}}{{100}}$. By substituting all the values $\dfrac{{22000 \times 5 \times 2}}{{100}} = 2200$.
Hence the correct option is (C) Rs. $2200$