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April 18, 2014

Posted by **holly** on Saturday, November 27, 2010 at 3:22pm.

Annual % Rate= 8

Time to Double??

Amount after 10 years= $20,000

I dont know how to figure out the initial investment and the time to double help me please?

- math -
**Person_blah**, Saturday, November 27, 2010 at 3:39pmI'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 -
**holly**, Saturday, November 27, 2010 at 3:44pmthank you XD that helped alot!!

- math -
**Person_blah**, Saturday, November 27, 2010 at 3:53pmGladly. Peace out.

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