Question

Find the simple interest on ${\text{Rs}}{\text{.10000}}$ for $2$ years at $10\% $ per annum.
A) $2000$
B) $2100$
C) $2200$
D) $2500$

Answer 1

Hint: As we know the formula for simple interest is given by the formula $\dfrac{{P \times R \times T}}{{100}}$ . And we are given that principal amount is, $P$ is equal to ${\text{Rs}}{\text{.10000}}$ , $T$ is the time period, that is given, $2$ years with rate $10\% $ per annum which is denoted by $R$.

Complete step-by-step answer:
Here, we are said to find the simple interest on ${\text{Rs}}{\text{.10000}}$ for $2$ years with the rate given $10\% $ per annum. So, simple interest is just like its name that simply the interest on the given amount over some period of time. For example, if someone has given $P$ rupees to someone at the interest rate of $R\% $ per annum, it means after one year that man has to pay him $P + R\% {\text{ of }}P$ , that is,
$P + \dfrac{{RP}}{{100}}$
And if he pays him back after $2$ years, then he has to pay him $P + 2\left( {R\% {\text{ of }}P} \right)$
$ = P + \dfrac{{2 \times R \times P}}{{100}}$
So here, this is the total amount but we get $\dfrac{{RP}}{{100}}$ and $\dfrac{{2RP}}{{100}}$. This is the simple interest .
As here, in example we saw that for $1$ year, simple interest is $\dfrac{{RP}}{{100}}$ and for $2$ years, simple interest is $\dfrac{{2RP}}{{100}}$ . Simple interest we got is $\dfrac{{2RP}}{{100}}$ and for $T$ years, simple interest would be $\dfrac{{P \times R \times T}}{{100}}$.
So, we got the formula for simple interest and that is equal to $\dfrac{{P \times R \times T}}{{100}}$
Where $P$ is the principal amount, $R$ is the rate and $T$ is the time period.
So here, in the question, we are given
Principal amount $P = {\text{Rs}}{\text{.10000}}$
Rate is given $10\% $ per annum and time is given for $2$ years per annum.
So, we can put in the formula of simple interest, i.e., $\dfrac{{P \times R \times T}}{{100}}$
Hence, simple interest $ = \dfrac{{10000 \times 10 \times 2}}{{100}} = {\text{Rs}}{\text{.2000}}$

Hence, option A is the correct answer.

Note: Here, we are given that amount is ${\text{Rs}}{\text{.10000}}$ and the rate is $10\% $ per annum. Then in one year, that amount increases to $10\% {\text{ of Rs}}.10,000$ that is
$
  10000 \times \dfrac{{10}}{{100}} \\
   = 1000 \\
 $
In the first year, simple interest will be ${\text{Rs}}.1000$ .
And for two years, it will be twice of one year, that is
$2 \times 1000 = 2000$.
For three years, it will be thrice of the first year, which is equal to
$3 \times 1000 = 3000$.