How long will it take for an investment to triple if it is compounded continuously at 15%?

Question

zepdrix · Answer

For continuous compounding, we use this relationship,$$\large\rm A=Pe^{rt}$$Where P is our principal investment,
r is the rate of compounding,
t is the amount of time that has passed,
and A is the amount we end up with.

Sound familiar? :)

hockeychick23 · Answer

yea but i only have the percent and that i want it to triple, so i dont really know what to do

zepdrix · Answer

So we want our amount that we end up with to be TRIPLE the principal that we started with. In other words, we our A value that we end up with is supposed to be $\large\rm 3P$.

So let's plug in what we know so far.

hockeychick23 · Answer

A= 3Pe^.15t

zepdrix · Answer

$$\large\rm 3P=Pe^{.15t}$$We'll plug this value in for A as well, k?
Next, divide both sides by P.

hockeychick23 · Answer

ok so 3= e^.15t

hockeychick23 · Answer

i got 7.32

zepdrix · Answer

Ok good good good.
That simplifies things a bit.
We're trying to solve for t, the time.
So we'll have to use logarithms to help get it out of the exponent position.

Oh, you got it already c:
Yayyyy good job \c:/

hockeychick23 · Answer

thanks!

zepdrix · Answer

So it will take just over 7 time periods for the amount to triple.
Whatever that time period may be, years or whatever.