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 -

    Gladly. Peace out.

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