Question

What is the difference between simple interest and compound interest on a principal amount of $10000$?

Answer 1

Step 1: Calculate the simple interest:

The formula of simple interest is $\mathit{S}\mathbf{.}\mathit{I}\mathbf{=}\frac{\mathbf{P}\mathbf{R}\mathbf{T}}{\mathbf{100}}$

Where $P$ is principal, $R$ is rate of interest and $T$ is time in year.

Given the principal amount is Rs.$10000$

Let the rate of interest is $10\%$ and the time duration of interest is $2$ years.

The simple interest for the given principal amount is,

$S.I=\frac{10000\times 10\times 2}{100}$

$\Rightarrow$ $S.I=2000$

Thus, the simple interest in a principal amount of $10000$ for $2$ years is Rs. $2000$.

Step 2: Calculate the compound interest

The compound interest for the given principal amount is,

$\mathit{C}\mathbf{.}\mathit{I}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}{\left[1+\frac{r}{100}\right]}^{\mathbf{T}}\mathbf{-}\mathit{P}$

$C.I=10000{\left[1+\frac{10}{100}\right]}^2-10000$

$\Rightarrow$ $C.I=10000{\left[1+0.1\right]}^2-10000$

$\Rightarrow$ $C.I=10000\left(1.21\right)-10000$

$\Rightarrow$ $C.I=12100-10000$

$\Rightarrow$ $C.I=2100$

Thus, the compound interest in a principal amount of $10000$ for $2$ years is Rs. $2100$.

Step 3: Find the difference between compound and simple interest

Hence, the difference between simple interest and compound interest on a principal amount of $10000$ is,

$\text{difference}=C.I-S.I$

$\Rightarrow$ $\text{difference}=2100-2000$

$\Rightarrow$ $\text{difference}=100$

Hence the difference between simple interest and compound interest on a principal amount of $10000$ is $100$.