# Math Help - Zack wishes to accumulate...

1. ## 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!

2. Originally Posted by tbl9301
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?

3. 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.

4. $
\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}}}}
$
$
= 50,000 \Leftrightarrow x \approx \ 519.7880156...
$

5. Originally Posted by jonah
$
\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}}}}
$
$
= 50,000 \Leftrightarrow x \approx \ 519.7880156...
$
Please repost, with a blank before and after the equal sign; thank you.