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Math Help - interest rates.

  1. #1
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    interest rates.

    I'm not sure if this belongs here or not- I am taking a contemporary mathematics course this semester and I missed a day of class. The name of the title is Finding interest rates.

    I already have the anwser, just need someone's help explaining how to solve the problem.
    For example: Suppose you invest $10,000 on your son's 13th birthday and it accumulates to 15,000 on his 18th birthday. What annual rate of compound interest did this investment earn?

    Pv=10,000 fv=15,000 t=5 years answer 8.45%

    Please help me.
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  2. #2
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    e^(i*pi)'s Avatar
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    The compound interest formula is F_v = P_v \left(1 + \dfrac{r}{n}\right)^{nt} where

    • F_v = Final Value
    • P_v = Initial Value
    • r = Annualised interest rate
    • n = number of compounds per year
    • t = number of years


    You know F_v = 15000, P_v = 10000, n = 1 (it's compounded annually) and t = 5

    Plug and Chug gives:

    r = \sqrt[5]{\dfrac{F_v}{P_v}} - 1
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by candisweet View Post
    I'm not sure if this belongs here or not- I am taking a contemporary mathematics course this semester and I missed a day of class. The name of the title is Finding interest rates.

    I already have the anwser, just need someone's help explaining how to solve the problem.
    For example: Suppose you invest $10,000 on your son's 13th birthday and it accumulates to 15,000 on his 18th birthday. What annual rate of compound interest did this investment earn?

    Pv=10,000 fv=15,000 t=5 years answer 8.45%

    Please help me.
    Well the compound interest formula is

    \displaystyle P=P_0\left(1+\frac{r}{n}\right)^{nt}

    and you are given P=15000,P_0=100000,n=1,t=5
    Putting all of this into the equation gives


    \displaystyle 15000=10000\left(1+r\right)^{5}

    Can you finish from here?

    Edit: too slow
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  4. #4
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    I know how to set the initial problem, but I guess what I'm asking is for the detailed steps because I cant figure it out, like how to isolate r, I think. Im so confused. Sorry math is not my thing.

    I get to here.

    15,000=10,000(1 + r) 5
    (15,000 /10,000 -1) = r 5
    don't know how to go further.
    Last edited by candisweet; February 22nd 2011 at 12:10 PM.
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  5. #5
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    e^(i*pi)'s Avatar
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    You have (1+r)^5 which is definitely not "r 5"

    I have solved the equation for r in post 2 (but note that you take the 5th root before subtracting 1)

    If your calculator does not have a 5th root button raise it to the power of 0.2
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  6. #6
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    Thanks. I wasn't using my calculator right. I got the answer! thanks so much
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  7. #7
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    REMEMBER: if a^p = b, then a = b^(1/p) ; TATTOO that on your wrist !
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