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Math Help - Zack wishes to accumulate...

  1. #1
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    Zack wishes to accumulate...

    Zack wishes to accumulate $50,000 in a fund at the end of 20 years. If he deposits $100 + x in the fund at the end of every 3 months for the first 10 years and $100 in the fund at the end of every 3 months for the second 10 years, find x to the nearest dollar if i(4) = .04.

    I think it's set up something like this: (100 + x)(a angle 40)(0.01) + (100)(a angle 40)(0.01) = 50000 , which equals (100 + x)((1-v^40)/.01) + 100((1-v^40))/.01) = 50000 with v=1/1.01
    ... but the answer is $520 so I might be totally off. Any help would be great thanks!
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  2. #2
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    Quote Originally Posted by tbl9301 View Post
    Zack wishes to accumulate $50,000 in a fund at the end of 20 years. If he deposits $100 + x in the fund at the end of every 3 months for the first 10 years and $100 in the fund at the end of every 3 months for the second 10 years, find x to the nearest dollar if i(4) = .04.

    I think it's set up something like this: (100 + x)(a angle 40)(0.01) + (100)(a angle 40)(0.01) = 50000 , which equals (100 + x)((1-v^40)/.01) + 100((1-v^40))/.01) = 50000 with v=1/1.01
    ... but the answer is $520 so I might be totally off. Any help would be great thanks!
    Just to be sure:
    Zack will NOT be depositing the additional $x dollars in the last ten years.

    Question:
    i(4) = .04.
    Is this intended to be the yearly interest rate?
    And by inference the quarterly rate is 0.01 and interest in computed and added quarterly to the fund?
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  3. #3
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    Correct, he will not be depositing the addition x in the last 10 years, only in the first 10. And yes I think since it is compounded quarterly the rate you use is .01.
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  4. #4
    Member jonah's Avatar
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    <br />
\left( {100 + x} \right)\frac{{\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4}  - 1}}{{{\textstyle{{0.04} \over 4}}}}\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4}  + 100\frac{{\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4}  - 1}}{{{\textstyle{{0.04} \over 4}}}}<br />
<br />
 = 50,000 \Leftrightarrow x \approx \$ 519.7880156...<br />
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  5. #5
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    Quote Originally Posted by jonah View Post
    <br />
\left( {100 + x} \right)\frac{{\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4} - 1}}{{{\textstyle{{0.04} \over 4}}}}\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4} + 100\frac{{\left( {1 + {\textstyle{{0.04} \over 4}}} \right)^{10 \times 4} - 1}}{{{\textstyle{{0.04} \over 4}}}}<br />
<br />
= 50,000 \Leftrightarrow x \approx \$ 519.7880156...<br />
    Please repost, with a blank before and after the equal sign; thank you.
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