2

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?

idknuttin
  • 2,525
  • When I use Wolfram Alpha I get 0.89889 which is pretty darn close to 0.9! I'd say the difference is due to rounding errors. – Bobson Dugnutt Feb 14 '16 at 22:44
  • I could have checked on wolfram also, I am asking if my math is correct? – idknuttin Feb 14 '16 at 22:45
  • 1
    I'd think so (finance isn't my strong suit); I don't think there's a formal difference between the continuous and daily in this instance, but let someone more knowledgeable answer that. – Bobson Dugnutt Feb 14 '16 at 22:47

1 Answers1

1

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

Community
  • 1
BCLC
  • 14,197