### 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 and 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 $$(I)$$ are 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.

$\begin{array}{l}I=\phantom{\rule{0.147em}{0ex}}\frac{P×n×r}{100};\\ \\ A=P+I\end{array}$

Substitute the "$$I$$" value in the above equation.

$A=P+\left(\frac{P×n×r}{100}\right)$

If we take the common term $$(P)$$ out then we will get:

$A=P×\left(1+\frac{n×r}{100}\right)$

$$\text{Amount} =$$ $$\text{Principal} +$$ $$\text{Interest}$$.

So, $$I = A – P$$.

Another formula can be derived based on $I=\frac{P×n×r}{100}$.

$r=\frac{100×I}{p×n}$

And, $n=\frac{100×I}{p×r}$$p=\frac{100×I}{r×n}$.