A certain sum amount 12167 in 3 years at 15% p.a compounded annually. Find sum.
Answer
383.7k+ views
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.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Which of the following Chief Justice of India has acted class 10 social science CBSE

Green glands are excretory organs of A Crustaceans class 11 biology CBSE

What if photosynthesis does not occur in plants class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

10 slogans on organ donation class 8 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE
