# Proof of simple interest formula

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!

• It should be $\Delta P=PRT$, not $I$. Then: $$I=P+\Delta P=P+PRT=P(1+RT).$$ – Tunk-Fey Apr 11 '14 at 15:55
• Well, then either $P=0$ or one of the two things you tell us are wrong. – mathse Apr 11 '14 at 15:55
• Dimensional analysis – evil999man Apr 11 '14 at 15:58
• @Awesome you wouldn't be able to distinguish between them with dimensional analysis: $$[M]\cong [M][T]^{-1}[T] + [M] \cong [M][T]^{-1}[T]$$ Where $[M]$ is units of money. – Thomas Russell Apr 11 '14 at 15:59
• @Tunk-Fey: Everywhere I see on the internet it says the $I = PRT$, not delta P. – OpieDopee Apr 11 '14 at 15:59

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.

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=$(pr/100)+(pr/100)+......................(pr/100)=(prt/100)$