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20 November, 16:43

find the interest rate for a $9000 deposit accumulating to $14,075.49, compounded quarterly for 9 years

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  1. 20 November, 20:40
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    Answer: The interest rate is 5%

    Solution:

    Deposit: D=$9,000

    Accumulating: A=$14,075.49

    Compounded quaterly→Number of periods per year: n=4

    Number of years: y=9

    A=D (1+r) ^ (ny)

    $14,075.49=$9,000 (1+r) ^ (4*9)

    $14,075.49=$9,000 (1+r) ^36

    Solving for r: Dividing both sides of the equation by $9,000:

    $14,075.49/$9,000=$9,000 (1+r) ^36/$9,000

    1.563943333 = (1+r) ^36

    Raising both sides to the power 1/36:

    1.563943333^ (1/36) = [ (1+r) ^36]^ (1/36)

    1.012499991 = (1+r) ^ (36*1/36)

    1.012499991 = (1+r) ^ (36/36)

    1.012499991 = (1+r) ^ (1)

    1.012499991=1+r

    Subtracting 1 both sides of the equation:

    1.012499991-1=1+r-1

    0.012499991=r

    r=0.012499991

    r=0.012499991*100%

    r=1.2499991%

    r=1.25% quarterly

    Annual interest rate: i=n*r

    i=4*1.25%

    i=5%
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