Find the rate of continuous compounding equivalent to daily compounding of 90%, if we assume that a year has 365 days.
P=principle
daily = $P(1+(\frac{0.9}{365}))^{365}$
continuous = $Pe^x$
$$(1+(\frac{0.9}{365}))^{365} = e^x$$
$$2.46=e^x$$
$$ln2.46=xlne$$
$$x=0.8989 \quad or \quad 89.89\%$$
Is $89.89\%$ continuous compounding equivalent to $90\%$ daily compounding?
I believe answer and solution are correct. This is just algebra. You've already shown basic understanding of advanced calculus concepts soooo.....
Btw, I think you should have said:
$A = P(1+(\frac{0.9}{365}))^{365\color{red}{t}}$
$A = Pe^{x\color{red}{t}}$
where $A$ denotes amount to owed to lender if $t$ under a certain type of compounding