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Math Help - what am i doing wrong?

  1. #1
    Junior Member
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    what am i doing wrong?

    Find the present value of an annuity that pays $6000 at the end of each 6-month period for 8 years if the interest rate is 8% compounded semiannually.

    According to my book, the answer is $69,913.77

    I don't understand why?
    according to my method i get another answer..

    An = 6000 [ 1- (1+0.01)^-16/.01 = 90,000

    what am i doing wrong?
    thanks.
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  2. #2
    Super Member

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    Hello, jhonwashington!

    Two errors . . .


    Find the present value of an annuity that pays $6000
    at the end of each 6-month period for 8 years
    if the interest rate is 8% compounded semiannually.

    According to my book, the answer is $69,913.77 .
    . . . Right!

    I don't understand why?
    according to my method i get another answer..

    An = 6000 [ 1- (1+0.01)^-16/.01 = 90,000 .
    . . . Incorrect formula

    . . and incorrect interest rate.

    The rate is 8% compounded semiannualy: . i \:=\:\frac{8\%}{2} \:=\:{\color{blue}0.04}


    The formula is: . {\color{blue}P \;=\;A\,\frac{(1+i)^n - 1}{i(1+i)^n}}

    And we have: . P \;=\;6000\,\frac{1.04^{16} - 1}{(0.04)(1.04^{16})} \;=\;69,\!913.77365...

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