Proof of simple interest formula

Question

Can someone please prove to me that $I = PRT$, where $P$ is the principal, $R$ is the interest rate, and $T$ is the number of years/time. I have seen $I = P(1+TR) = P+PTR$ which does not equal $PRT$, so I am slightly confused. Any help is appreciated, Thanks!

Answer 1

You have for simple interest at a fixed interest rate per time period $R$:

$$I=\sum_{i=1}^{T}PR=PRT$$

Where $I$ is the total interest after $T$ time periods. Therefore your other formula should read:

$$P(T)=P(0)(1+RT)$$

Where $P(T)$ is the principle after $T$ time periods.

Answer 2

For 100 we get $r$,then for $p$ we get $(pr/100)$,first time, same thing we will get after 2nd year similarly 3rd, therefore

s.i after $t$ time=$(pr/100)+(pr/100)+......................(pr/100)=(prt/100)$