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Math Help - Interest Rate

  1. #1
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    Interest Rate

    Find the interest rate needed for an investment of $7,000 to grow to $10,500 in 6 yr if interest is compounded monthly. (Round your answer to the nearest hundredth of a percentage point.)
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  2. #2
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    You are supposed to show some effort. Do you know the formula for the total amount after n month? If yes, what is your difficulty?
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  3. #3
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    a = p (1+ r/m) ^mt
    ??
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  4. #4
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    Yes, so 10500=7000(1+r/12)^{12\cdot6}, i.e., (1+r/12)^{72}=1.5. By raising both sides to 1/72, you can find r.
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  5. #5
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    idk how to take the log and find r...
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  6. #6
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    do u want me to take 72th root of both sides?
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  7. #7
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    if i take the 72th root of both sides then r = 0 ...?
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  8. #8
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    if i take the 72th root of both sides then r = 0 ...?
    No, if (1+r/12)^{72}=1.5, then 1+r/12=(1.5)^{1/72}=\sqrt[72]{1.5}\approx1.00565.
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  9. #9
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    ok i got it..
    thanks the answer came out right..
    r = 6.80 rounded
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  10. #10
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    But the other problem i am not able to figure out and i have 1 more try left its the last one..
    can you please help
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  11. #11
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    Use logarithms to solve the equation for t.
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  12. #12
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    \displaystyle\frac{A}{1+Be^{t/2}}=C iff
    A=C(1+Be^{t/2}) and 1+Be^{t/2}\ne0.

    A=C(1+Be^{t/2}) iff
    A=C+BCe^{t/2} iff
    A-C=BCe^{t/2} iff
    (A-C)/(BC)=e^{t/2} or (A-C=0 and B=0).

    (A-C)/B=e^{t/2} iff
    \ln((A-C)/(BC))=t/2.
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  13. #13
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    SO T = 2ln((A-C)/BC))

    right?
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  14. #14
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    yessssssss its right!!!

    thankkkk kyouuuuu soo muchhhh i appreciate your help very muchhhhh
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  15. #15
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    You are welcome.
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