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!
Asked
Active
Viewed 2,566 times
1
-
1It 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
-
1Dimensional 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
-
And a bit common sense...we can always use the keyword "obviously" – evil999man Apr 11 '14 at 15:59
-
Ah never mind, I just figured it out :P Silly question – OpieDopee Apr 11 '14 at 16:04
2 Answers
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.
Thomas Russell
- 10,425
- 5
- 38
- 66
