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Math Help - present value

  1. #1
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    present value

    Find the present value to the nearest dollar on January 1 of an annuity which pays $2,500 every month for 10 years. The first payment is due on the next April 1 and the rate of interest is 11% convertible monthly.


    the answer i got was 24104.02971, can anyone pls help confirm this with steps..thanks
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  2. #2
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    Hello, actsci231!

    The wording is confusing . . .


    Find the present value to the nearest dollar on January 1 ?
    of an annuity which pays $2,500 every month for 10 years.
    The first payment is due on the next April 1 ?
    and the rate of interest is 11% convertible monthly.

    The answer i got was 24104.02971.
    Can anyone pls help confirm this with steps? Thanks
    I don't understand the use of dates.
    . . And what do they mean by "first payment is due"?


    I interpret the problem like this:

    We want to collect $2500 per month, starting next month.

    We will deposit a sum of money (present value) now
    . . and get 11% interest, compounded monthly.


    Formula: . P \;=\;A\cdot\frac{(1+i)^n - 1}{i(1+i)^n} . where: . \begin{Bmatrix}P &=&\text{present value} \\ A &=& \text{amount of payment} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}

    We have: . A = 2500,\;\;i = \frac{11\%}{12} = \frac{0.11}{12},\;\;n = 120

    Hence: . P \;=\;2500\cdot\frac{\left(1+\frac{0.11}{12}\right)  ^{120}-1} {\frac{0.11}{12}\left(1 + \frac{0.11}{12}\right)^{120}} \;=\;181,\!488.1886


    Therefore, we must deposit $181,488 now.

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  3. #3
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    me too i dont the wording...but the january 1 is when he deposits the money, and im assuming the first payment thing is when the interest starts to compound so i did it like

    2500 [( v^118 - 1)/(v - 1)]

    but im not sure if i did this correctly, thanks for the reply
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  4. #4
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    On March 1, one month before the first payment is due, the value of your annuity is
    <br />
A = 2,500 \cdot \frac{{1 - \left( {1 + \tfrac{{.11}}<br />
{{12}}} \right)^{ - \left( {10 \times 12} \right)} }}<br />
{{\tfrac{{.11}}<br />
{{12}}}} \approx \$ 181,488.1884<br />
    which is the same as Soroban’s results.
    On January 1, two months before March 1, the present value or the discounted value of your annuity is given by
    <br />
P = A\left( {1 + \tfrac{{.11}}<br />
{{12}}} \right)^{ - \left( {\tfrac{2}<br />
{{12}} \times 12} \right)}  \approx \$ 178,206.1023<br />
    Last edited by jonah; October 16th 2008 at 08:38 AM. Reason: grammar correction
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  5. #5
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    but doesnt payment start in april
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