# A certain sum amount 12167 in 3 years at 15% p.a compounded annually. Find sum.

Last updated date: 17th Mar 2023

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Answer

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Hint: Here we go through by putting the formula of amount as we read in chapter compound interest because we have to find the sum i.e. principal amount and at the end of three years total amount is given i.e. certain sum.

Complete step-by-step answer:

Here in the question it is given that a certain amount is Rs.12167 i.e. the given Amount (A) =RS.12167

The given time period (T) =3 years.

And the given rate(R) =15% compounded annually.

Let us apply the formula of amount in which rate is compounded annually i.e. \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]

Now put the values in the formula and find out the unknown term.

\[

\Rightarrow 12167 = P{\left( {1 + \dfrac{{15}}{{100}}} \right)^3} \\

\Rightarrow 12167 = P{\left( {\dfrac{{23}}{{20}}} \right)^3} \\

\Rightarrow P = \dfrac{{12167 \times 20 \times 20 \times 20}}{{23 \times 23 \times 23}} \\

\Rightarrow P = Rs.8000 \\

\]

Hence the required answer is Rs.8000.

Note: Whenever we face such a type of question the key concept for solving the question is just simply put the formula in which the given terms of question are used and find out the unknown term that question asked by the help of that formula. Here in this question the amount, time and rate are given and we have to find the principal amount. So we apply the formula of amount.

Complete step-by-step answer:

Here in the question it is given that a certain amount is Rs.12167 i.e. the given Amount (A) =RS.12167

The given time period (T) =3 years.

And the given rate(R) =15% compounded annually.

Let us apply the formula of amount in which rate is compounded annually i.e. \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]

Now put the values in the formula and find out the unknown term.

\[

\Rightarrow 12167 = P{\left( {1 + \dfrac{{15}}{{100}}} \right)^3} \\

\Rightarrow 12167 = P{\left( {\dfrac{{23}}{{20}}} \right)^3} \\

\Rightarrow P = \dfrac{{12167 \times 20 \times 20 \times 20}}{{23 \times 23 \times 23}} \\

\Rightarrow P = Rs.8000 \\

\]

Hence the required answer is Rs.8000.

Note: Whenever we face such a type of question the key concept for solving the question is just simply put the formula in which the given terms of question are used and find out the unknown term that question asked by the help of that formula. Here in this question the amount, time and rate are given and we have to find the principal amount. So we apply the formula of amount.

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