math
posted by holly on .
Initial Investment??
Annual % Rate= 8
Time to Double??
Amount after 10 years= $20,000
I don't know how to figure out the initial investment and the time to double help me please?

I'll try to help. I'm not exactly sure if the money is being compounded continuously or not but I'll guide you along with the assumption that it is.
Pe^(rt) = current amount of money
P = principal
e = natural base = about 2.71
r = rate (.08 in this case)
t = time... in years
(^ is exponentiation by the way)
Since we know the amount after 10 years = $20000, we can easily solve for P
P = 20000/(e^(.08*10))  about $9009.
For the time to double. Imagine that you initialy invested $1. Just one into the bank account.
The amount you want eventually is $2, right? (Duh, it has to double.)
2 = 1(e^(.08)*t)
Take the natural log of both sides. ln. It gets rid of the e.
ln 2 = ln (e^(.08 *t))
Based on properties of log and natural log, the .08*t is left behind on the right.
ln 2 = .08*t
t = ln 2/.08 = about 8.66 years
(For doubling problems, you can always check your answers by using the rule of 72. For instance, since the rate is 8%, divide 72 by that. You should get 9. That's kinda close to the time you got, right? Don't use this as a replacement for doing the actual work, but if you're ever unsure, you can use this method to check.) Hope this helped. Peace out. 
thank you XD that helped alot!!

Gladly. Peace out.