Question

Find the amount and compound interest on $Rs.9000$ for 2 years 4 months at $10\% $ per annum compounded annually.

Answer 1

Hint: In this formula, we have been given a principal amount, rate of interest and the time and we have been asked to find the amount and interest. Use the compound interest formula and put all the given details. You will get the final amount. Subtract this from the given principal amount and you will get the compound interest.

Formula used: $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$, where $A = $Amount, $P = $Principal amount, $R = $Rate of interest and $N = $number of years invested.

Complete step-by-step solution:
We are given the principal amount, rate of interest and the time and we have to find the amount and interest.
Given is,
1) $P = 9000$
2) $R = 10\% $
3) $N = $2 years 4 months
Mathematically, time can be represented as -
\[N = 2 + \dfrac{4}{{12}} = 2 + \dfrac{1}{3} = \dfrac{7}{3}\]years
Now, we can put all the information in the formula.
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
$ \Rightarrow A = 9000{\left( {1 + \dfrac{{10}}{{100}}} \right)^{\dfrac{7}{3}}}$
Shortcut for calculation: If we write $\dfrac{7}{3}$ in decimals, we will get $2.\bar 3$. It simply means 2 and $\dfrac{1}{3}$ times. So, we will multiply $\left( {1 + \dfrac{{11}}{{10}}} \right)$ two times and for that $\dfrac{1}{3}$rd part, we will multiply $\left( {1 + \dfrac{{11}}{{10}}} \right)$ by $\dfrac{1}{3}$ in the shown way.
Moving back to the question,
$ \Rightarrow A = 9000{\left( {1 + \dfrac{{10}}{{100}}} \right)^2}\left( {1 + \dfrac{{\dfrac{1}{3} \times 10}}{{\dfrac{{100}}{1}}}} \right)$
Simplifying the equation,
$ \Rightarrow A = 9000 \times \dfrac{{11}}{{10}} \times \dfrac{{11}}{{10}} \times \left( {1 + \dfrac{1}{{30}}} \right)$
$ \Rightarrow A = 9000 \times \dfrac{{11}}{{10}} \times \dfrac{{11}}{{10}} \times \dfrac{{31}}{{30}}$
On multiplying and dividing, we will get –
$ \Rightarrow A = 11253$
Therefore, the final amount is $Rs.11,253$.
In order to find the compound interest, we will have to subtract the principal amount from the final amount.
$ \Rightarrow C.I = A - P$
$ \Rightarrow C.I = 11253 - 9000 = 2253$
Hence, compound interest is $Rs.2253$.

Note: 1) Students often get confused between simple interest and compound interest. It should be kept in mind that compound interest formula gives us the final amount whereas the simple interest formula gives us the interest.
2) You can also use the formula to get the interest directly and not the amount-
$ \Rightarrow C.I = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} - P$
This formula will give you interest.