# What amount will sum up to Rs.12100 at \[10\%\] per annum in Compound Interest in \[2years\]?

(A) 10,000

(B) 11,000

(C) 9,000

(D) 8,000

Answer

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**Hint:**We are given a compounded interest of a certain amount which at \[10\%\] per annum in \[2years\] gives a total of Rs.12100. And we are asked in this question to find that certain amount, that is, we have to find the principal amount. We will use the formula of the compound interest, which is, \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]. So, we have to find P, which is the principal amount. We are given \[A=Rs.12100\], \[R=10\%\] and \[T=2years\]. So, we will substitute these values in the formula of compound interest and we will get the required value of the amount.

**Complete step-by-step solution:**

According to the given question, we are given that a certain amount when compounded for 2 years at the rate of \[10\%\] per annum gives the total sum as Rs.12100. We are asked in the question to find the starting or the so called - principal amount.

In order to solve for principal amount, we will use the formula of compound interest and we have it as follows:

\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]

Here, A is the compounded value on the amount which in our case is Rs.12100.

P is the principal amount which we have to find.

R is the rate of interest of the compound interest, which is, \[10\%\]

And T is the time period, which is, \[2years\]

We will now substitute these values in the above formula and we get,

\[\Rightarrow 12100=P{{\left( 1+\dfrac{10}{100} \right)}^{2}}\]

Simplifying the above expression, we get,

\[\Rightarrow 12100=P{{\left( 1+\dfrac{1}{10} \right)}^{2}}\]

Taking the LCM in the bracket of the above expression and we have,

\[\Rightarrow 12100=P{{\left( \dfrac{10+1}{10} \right)}^{2}}\]

\[\Rightarrow 12100=P{{\left( \dfrac{11}{10} \right)}^{2}}\]

\[\Rightarrow 12100=P\left( \dfrac{121}{100} \right)\]

We will now write the above expression in terms of P, and we get,

\[\Rightarrow P=12100\times \dfrac{100}{121}\]

Cancelling out the similar terms in the above expression, we get,

\[\Rightarrow P=100\times 100\]

So, we get the value of the principal amount as,

\[\Rightarrow P=Rs.10000\]

**Therefore, the principal amount is Rs.10,000.**

**Note:**The formula for the simple interest is as follows, \[S.I=\dfrac{P\times R\times T}{100}\], where P is the principal amount, R is the Rate of interest and T is the time period. Do not get confused with simple interest for compound interest Both are different from each other. Also, while substituting the values in the formula of compound interest, the values must be correctly substituted without misplacing any terms.

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