Determine how much time is required for an investment to double in value if interest is earned at a rate of 6.25% compounded continuously ?

Question

anonymous · Answer

what is continuously?

anonymous · Answer

Hmmm I would say every single day so its compounded 365 days
But lemme just ask inquire with @dumbcow 

Either way there is an equation to determine the Effective Annual Rate when its compounded continuously aka daily 365 days a year

The formula is as follows
$$e^{r}-1=e^{.0625}-1=.0645$$
This is equivalent to 6.45%

anonymous · Answer

So assuming that we have an EAR of 6.45 % we can have the following formula
Lets say our investment is "a"
We start off with "a" and we are wondering how long it will take till our investment doubles to 2a
Lets use our regular folrmula
$$2a=a(1+.645)^x$$

Solve for x

Do you follow what I have done???
Any questions?

dumbcow · Answer

@wahahaha , compound continuously is even more than 365 days, its like every second
but just use the "e" and you are fine

to double you want growth to be factor of 2
$$e^{.0625 t} = 2$$
$$t = \frac{\ln 2}{.0625}$$

anonymous · Answer

@dumbcow Yaaaa okkk Its just a branch off of what I did above but just in a more efficient manner
K thanks

dumbcow · Answer

yeah you are not wrong, but you will have a rounding error

anonymous · Answer

Ok I gotcha ... Thanks

anonymous · Answer

thanks to you both!