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Interest rate calculation help

  1. Sep 19, 2005 #1
    i am having problems figuring out how to find the answer to this problem:

    nancy wants to invest $4000 in saving certificates that bear an interest rate of 9.75% per yr, compound semiannually. how long a time period should she choose inorder to save an amt of $5000?

    the answer is approximately 2.3 yrs. i am not sure how to get this answer. pleasssseee help!!!!!!
     
  2. jcsd
  3. Sep 19, 2005 #2

    TD

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    What have you tried?
    Do you know how to set up the equation somewhat?
     
  4. Sep 19, 2005 #3
    i think you use the equation Ao(1+r/n)^nt: i think this one is it.
    or Ao e^rt (growth)
     
  5. Sep 19, 2005 #4

    TD

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    Well, we have 4000 at the start and it increased by 9.75 percent, which we can express by multiplying with 1.0975, this for each year. We also know what we want to end up with, so we get the equation: [tex]4000 \cdot 1.0975^n = 5000[/tex]

    Here, n is the number of years. Now, could you solve it?
     
    Last edited: Sep 19, 2005
  6. Sep 19, 2005 #5
    how does that end up being 2.3 years
     
  7. Sep 19, 2005 #6

    Päällikkö

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    [tex]n = \frac{ln(\frac{5000}{4000})}{ln(1,0975)}[/tex]
     
  8. Sep 19, 2005 #7

    TD

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    Indeed, and that's approximately 2.39 (so I'd say 2.4 when rounding...)
    Since the interest comes semianually, to get (at least) the 5000 you have to wait 2.5 years.
     
  9. Sep 19, 2005 #8
    where did you get 1.0975 from?
     
  10. Sep 19, 2005 #9

    TD

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    Didn't you read post #4? I already included the equation for you :smile:
     
  11. Sep 19, 2005 #10
    okayyyy! Thanks!!! :rofl:
     
  12. Sep 19, 2005 #11

    TD

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    No problem :smile:

    But since you didn't set it up yourself, I hope you do understand it?
    If not, don't hesitate to ask for further details!
     
  13. Sep 19, 2005 #12
    the only reason i was wondering was because if you set it up in the equation i gave you it would be (1+9.75/2)^2T,,,i think
     
  14. Sep 19, 2005 #13

    TD

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    Well I don't fully understand that one, where did you get the "2" for n?
     
  15. Sep 19, 2005 #14
    because the rate of interest in compounded semiannually
     
  16. Sep 19, 2005 #15

    TD

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    Then, I think, the equation should be:

    [tex]4000\left( {1 + \frac{{0.0975}}
    {2}} \right)^{2t} = 5000[/tex]

    That gives approx 2.34

    I assume this is correct, because in my earlier equation we didn't use the fact that the interest was semianually.
     
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