Question

If \[8000\] is invested at $6$ percent simple annual interest, how much interest is earned after 3 months?
$
  \,A\,)\,120 \\
  \,B\,)\,280 \\
  \,C\,)\,240 \\
  \,D\,)\,160 \\
 $

Answer 1

Hint:
Convert the percent of interest rate into decimal parts. Then substitute the given values in the formula to find the value of total interest. Then multiply the obtained answer with the number of months given in the question to find the answer.

Useful Formula: The formula which is used to find the total interest is $\text{Interest} = \text{Principle amount} \times \text{Interest Rate} \times \text{time}$ . Divide the given interest rate by $100$ before substituting the formula.

Complete step by step solution:
Given that, the annual interest given in the question is $6\,\% $ and the principal amount invested is $8000$.
To find that the simple interest earned after $3$ is invested.
Let us assume $p$ as that amount invested at $6$ percent simple annual interest is
$p\, = \,8000$
Now, modify the simple annual interest of $6\,\% $ by the decimal part.
Already the simple interest is in the fractional part, modify it to the decimal part.
Consider the given interest as ${I_1}$,
${I_1}\, = \,6\,\% $
Percent is nothing but the number divisible by $100$,
${I_1}\, = \,\dfrac{6}{{100}}$
Now, simplify the ${I_1}$by decimal part as follows:
${I_1}\, = \,0.06$

The interest which is calculated as follows:
$\text{Interest} = \text{Principle amount} \times \text{Interest Rate} \times \text{time}$
Here,
Principle amount $ = \,8000$
Interest rate $ = \,0.06$
Time $ = \,1$

Substitute the above given details in the formula as follows:
$\text{Interest} = \text{Principle amount} \times \text{Interest Rate} \times \text{time}$
Interest $ = \,8000\, \times \,0.06\, \times \,1$
Simplify the above equation:
Interest $ = \,480.00\,$
No need to consider the zero values after decimal, then the equation becomes
Interest $ = \,480$
Thus, the total interest for the given question is $480$.

Now, we want to find the interest when same amount is invested after $3$ months:
We can modify the $3$ months as $\dfrac{3}{{12}}$, which is nothing but $1$ year contains $12$ months:
To find the interest which after 3 months invested, multiply $\dfrac{3}{{12}}$ with the total interest that we calculated:
Interest = $\dfrac{3}{{12}}\, \times \,480$
Simplify the above equation by cancelling the $480$ by $12$ and multiply the obtained answer with $3$
Interest = $3\, \times 40$
The final obtained answer is Interest = $120$

Thus, the option $\,A\,)\,120$ is the answer for the interest after 3 months invested.

Note:
Remember that the interest rate always should be divisible by $100$. The number of months should always be divided by $12$. It is just the matter of understanding and representation that percentage interest can also be a fraction or decimal. 25% interest can be represented as $\dfrac{1}{4}$ in fraction whereas in decimal it could be $0.25 \%$.