### Theory:

Simple Interest ($$I$$):
• Simple interest is a quick and easy method of calculating the interest charge on loan.
• Simple interest is determined by multiplying the interest rate by the principal by the number of days that elapse between payments.
• This type of interest usually applies to automobile loans or short-term loans,
Derivation of the formula to calculate the Simple interest ($$I$$):

First, take $$P$$ as the principal or sum and $$r\%$$ as a rate percent per annum. On every $$₹100$$ borrowed the interest paid is $$₹r$$.

Therefore, on $$₹P$$ borrowed the interest paid for one year would be $=\phantom{\rule{0.147em}{0ex}}P×1×\frac{r}{100}$.

Then the interest period for two years $=\phantom{\rule{0.147em}{0ex}}P×2×\frac{r}{100}$.

Then the interest period for three years $=\phantom{\rule{0.147em}{0ex}}P×3×\frac{r}{100}$ and so on.

If the time period is '$$n$$ ' number of years, the formula will be $I=\frac{P×n×r}{100}$.

Basic Formulae:

Amount ($$A$$) :
If the principal amount (P) and simple interest (I) is given, then we can find out the amount by adding the principle and simple interest.
$A=P+I$

Simply rearranging both the formula as per requirement we can find all the variants in the formula.

$\begin{array}{l}I=\phantom{\rule{0.147em}{0ex}}\frac{P×n×r}{100};\phantom{\rule{0.147em}{0ex}}A=P+I\\ \\ \mathit{Substitute}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}I\phantom{\rule{0.147em}{0ex}}\mathit{value}\phantom{\rule{0.147em}{0ex}}\mathit{in}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{above}\phantom{\rule{0.147em}{0ex}}\mathit{equation}.\\ A=P+\left(\frac{P×n×r}{100}\right)\\ \\ \mathit{If}\phantom{\rule{0.147em}{0ex}}\mathit{we}\phantom{\rule{0.147em}{0ex}}\mathit{take}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{common}\phantom{\rule{0.147em}{0ex}}\mathit{term}\phantom{\rule{0.147em}{0ex}}P\phantom{\rule{0.147em}{0ex}}\mathit{out}\phantom{\rule{0.147em}{0ex}}\mathit{then}\phantom{\rule{0.147em}{0ex}}\mathit{we}\phantom{\rule{0.147em}{0ex}}\mathit{will}\phantom{\rule{0.147em}{0ex}}\mathit{get}:\\ A=P+\left(1+\frac{n×r}{100}\right)\\ \\ \mathit{We}\phantom{\rule{0.147em}{0ex}}\mathit{know}\phantom{\rule{0.147em}{0ex}}\mathit{that}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{Amount}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{Interest}\phantom{\rule{0.147em}{0ex}}\left(I\right)\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}\mathit{Principal}\left(P\right)\\ \\ \mathit{So}\phantom{\rule{0.147em}{0ex}}I=A-P\end{array}$

Another formula can be derived based on $I=\frac{P×n×r}{100}$.
$\begin{array}{l}r=\frac{100×I}{p×n}\\ \\ \mathit{And}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}n=\frac{100×I}{p×r}\\ \\ p=\frac{100×I}{r×n}\end{array}$