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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. $1250$
(C)Rs. $2200$
(D)Rs. $2300$

Last updated date: 20th Jun 2024
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Hint:As we know that the above question consists of both compound interest and simple interest. Simple interest can be defined by interest calculated on the principal portion of a loan while we can define compound interest as the interest calculated on the principal and the interest accumulated over previous time. In this question the principal is not given, so we will calculate it by the formula of compound and simple interest.

Complete step by step solution:
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. $2200$

Note: Before solving this kind of question we should know what is simple interest and compound interest. WE should be aware of all their formulas and be careful what the question is asking i.e. is it simple interest or compound interest. WE should know that the major difference between the simple interest and compound interest is that simple interest is based on the principal of the deposit or a loan while compound interest is based on the principal and interest that accumulates in a period of time.