Question

Calculate the compound interest on Rs 18,000 in 2 years at $15\% $ per annum.

Answer 1

Hint: In this, we will simply use the compound interest formula and put the values in the formula and this is how we will find the interest. We will put the principle, time and per annum percentage, and the price in the formula, it will give us the amount, to get compound interest we subtract the principle from the amount, hence we get the answer.

Complete step-by-step solution:
By given question, we will get
Principle, $P = 18000$
Time, $N = 2$
Rate of interest, $R = 15\% $
Now we will be using the compound interest formula, which is given below
Here we can see that principle, interest, and amount of time, everything is given, so it will get easier to solve by just putting the values in their place in the formula
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}$
Now we will put all values in the compound interest formula according to given
So, we have,
$ \Rightarrow A = 18000{\left( {1 + \dfrac{{15}}{{100}}} \right)^2}$
Cancel out the common factor in the bracket,
$ \Rightarrow A = 18000{\left( {1 + \dfrac{3}{{20}}} \right)^2}$
Taking LCM in the bracket we get,
$ \Rightarrow A = 18000{\left( {\dfrac{{20 + 3}}{{20}}} \right)^2}$
On adding the terms, we get
$ \Rightarrow A = 18000{\left( {\dfrac{{23}}{{20}}} \right)^2}$
On Simplifying the terms, we get
$ \Rightarrow A = 18000 \times \dfrac{{23}}{{20}} \times \dfrac{{23}}{{20}}$
Cancel out the common factors,
$ \Rightarrow A = 45 \times 23 \times 23$
Now, multiply the terms,
$ \Rightarrow A = 23805$
As we know, compound interest is Amount minus the principle,
$C.I. = A - P$
On substituting the values, we get
$ \Rightarrow C.I. = 23805 - 18000$
On simplification we get,
$\therefore C.I. = 5805$

Hence, the compound interest is Rs 5805.

Note: Compound interest is the interest paid on the original principal and on the accumulated past interest. This is very important in banks and investments. An important part of taking a loan from the bank is how we calculate compound interest accordingly. Every bank has a different interest rate.