# math

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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?

• math - ,

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.

• math - ,

thank you XD that helped alot!!

• math - ,