Simple Interest Formulas

Simple interest formula:

Simple Interest = $\dfrac{{PTR}}{{100}}$
P = Principal
T = Time
R = Rate of Interest

Simple interest for 1 year = Principal × (Interest %) = P × (R%)
If simple interest for more than 1 year the Simple interest = $P \times R\%  \times T = SI$
Interest % = $\displaystyle\frac{\text{Interest}}{{{\rm{Principal}}}} \times 100 = \displaystyle\frac{\text{SI}}{{\text{P}}} \times 100$

Concept of Installments:

Why someone gives installment paying for a buyer?  It gives some flexibility for the buyer if he gets income on a monthly basis.  Is there any advantage for the seller? Let us see how the installment works!
Suppose, there is a mobile phone for sale at Rs.10,000.  There are two options for the seller. Accepting full money of Rs.10000 in one go, or take some down payment and receiving the remaining amount in "equated monthly/yearly installments".
If the seller receives the total amount on the purchase, he gets some interest on the sale money.  If he sells it at monthly installment, he makes sure that he sets the installments such that he recovers the interest in several installments.
So the logic works like this:  If the seller sold a product for t months,  Total amount + interest he gets for  t months on sale price = Total installments + interests generated on this installments for the remaining period.

For example, if the total loan for 5 months, the seller gets 4 months interest on the 1st installment, 3 months interest on the 2nd installment, 2 months interest on the 3rd installment, 1 month interest on the 4th installment, no interest on 5th installment.
$P + \dfrac{{P \times t \times R}}{{100 \times 12}}$ = $\left( {x + \dfrac{{x \times (t - 1) \times R}}{{12 \times 100}}} \right)$ + $\left( {x + \dfrac{{x \times (t - 2) \times R}}{{12 \times 100}}} \right)$ + . . . . . + $\left( {x + \dfrac{{x \times R \times 2}}{{12 \times 100}}} \right)$ + $\left( {x + \dfrac{{x \times R \times 1}}{{12 \times 100}}} \right)$ + $x$
Note: The above formula is for monthly installments. If installment is asked per year, then no need to divide those terms with 12
General formula for installment calculation: \(x = \dfrac{{P\left( {1 + \dfrac{{n \times r}}{{100}}} \right)}}{{n + \dfrac{{n(n - 1)}}{2} \times \dfrac{r}{{100}}}}\)
(Note: If you calculating monthly installments, replace "n" by number of months, and "r" by "r/12"
After simplification of the above formula, you get \(x = \dfrac{{P\left( {100 + nr} \right)}}{{100n + \dfrac{{n(n - 1)r}}{2}}}\)