I've watched the khan academy pre-calculus playlist about compound interest and constant e on youtube Khan Academy. First he said that you can compute the final payment like this:
Let P = Principal, let r = interest rate in decimal, let t = time period, let F = final payment, then the equation would be like this:
$P(1 + r)^t = F$
For example if I borrowed \$50 for 1 year for 15%, then after 20 years I would need to repay \$818.
But then he says that this equations equals to this:
But this is not completely equal to the other equation. Can you explain me what did he mean by this last equation, is this equation even right?