Formula Derivation

[SniperAssault]

Hi there, I saw this picture from Facebook in one of our group discussions and it seemed that there was something off in here:



I could be wrong but doesn't step 2 contradict the premise that P1 = P0*e^rt? Thanks in advance.

 

[HallsofIvy]

No, there is no contradiction- and certainly not in step 2! Step 2 just says "P1= 2P" with no mention of P0. It is step 3 you should refer to- it actually says "P1= 2P0" and you want to compare that to \(\displaystyle P1= P0e^{rt}\). Those are not contradictory because of that parameter "rt". In fact the rest of the calculation is finding rt so they are NOT contradictory. In order to have both P1= 2P0 and \(\displaystyle P1= P0e^{rt}\) then we must have \(\displaystyle 2P0= P0e^{rt}\) which reduces to \(\displaystyle 2= e^{rt}\) or \(\displaystyle rt= ln(2)\). As long as r and t as such that their product is ln(2), those statements, P1= 2P0 and \(\displaystyle P1= P0e^{rt}\) will be exactly the same, not contradictory,