What annual rate of interest compounded continuously is required to double an investment in 5 years?

You can approximate this using the rule of 72, this is

72/Rate = Time Required to Double Your Money

Thus at 5% u get

72/5 = approx. 14 years

Edit: Oops!! l answered the wrong question above. the solution to ur question is below.

2e^r5 = 4
ln2 + lne^r5 = ln4
ln2 + r x 5 =ln4
.6391 + r x 5 = 1.3863
r x 5 =.7472
r = .7472/5
r = .1494

Your required yield would be 14.94%

Aronoda -- hey l was rushing & misinterpreted the question, nobodies perfect. Anyhow, check out the second answer & try to talk crap, if u can even understand how l derived the answer. And no, OP said continuous compounding (there is such a thing) & did not mention anything about after tax returns.

Edit: Whatever jaymay that is why l practice -- u preach. You goddam academics think ur so smart, yet u do not even engage in what u teach, then u question guys in the trenches like me for posting an answer online that was off a hair -- you've probably never managed a dime of institutional money. Bunny, yes it is true, jaymay is answer is more accurate than mine, by about .01 percent. Nevertheless, my answer is still correct except for the final step of taking the ln of my answer, so call it a rushed approximation. Jaymay, u can blow me, my bonus is bigger than ur salary. If u want to try to attack my credibility as an analyst because my answer was off a hair, then u can just go to hell & take ur chalk & text books with you, loser, LOL!

14.4%

wow that analyst gets paid?
l think the rule of 72 assumes annual compounding and it doesnt assume taxes. Do you mean compounded daily?

Edit:Lol woah there man l was just messing with ya. l was under the impression the rule of 72 didnt use continuous. guess l was wrong my bad

Edit: OOOOOOOOOOOOOOOOOOOOO! Analyst u got owned!!!! jk man ive been reading ur comments you know what ur talking about :-)

hi beachbunny

first of all, let me explain WHY AMERICA is in trouble. It is because people like the ''BIG SHOT FINANCIAL ANALYST'' who answered ur basic question IS WRONG. Then he states that ''he gets paid to know this ''crap'''' & that is why America is currency is in the toilet as well.

Bashing aside, l have been a financial math teacher for decades & the answer to ur question is 13.86%.

Basically we find the effective rate is 14.87% & then we take the natural logarithm of this number, i.e. In(1.1487) = .1386 which is 13.86%

So the CORRECT ANSWER is 13.86% & this rate IS compounded continuously

best of luck.