help | Mathematics | Page 1

vivid ledge Jul 18, 2025, 7:52 PM

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A couple decides on the following plan for their newborn child's college education. Every 3 months, they will deposit $1,000 into a savings account paying 3.4% interest compounded quarterly. However, after 8 years, they are unable to deposit any more money into the account. They stop making deposits and let the money accumulate interest at the same rate for 15 more years. How much money will be in the account at the end of the 23 years?

(Hint: You will need to use two different formulas to answer this question.)

unkempt boneBOT Jul 18, 2025, 7:52 PM

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trim sage Jul 18, 2025, 8:10 PM

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!status

unkempt boneBOT Jul 18, 2025, 8:10 PM

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

trim sage Jul 18, 2025, 8:16 PM

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@vivid ledge

vivid ledge Jul 18, 2025, 8:16 PM

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i got my answer wrong and i need help with it

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60814.34

trim sage Jul 18, 2025, 8:16 PM

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Show me your work

vivid ledge Jul 18, 2025, 8:17 PM

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1000*((1+.034/4)^32-1))/.034/4 = 36597.53664245

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36597.53664* (1+.034/4)^60 = 60814.34

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used p=(1+r/n)^nt-1/(r/n) as first forula

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a= p(1+r/n)^nt as second formula

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@trim sage

trim sage Jul 18, 2025, 8:21 PM

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Use the geometric series formula

vivid ledge Jul 18, 2025, 8:21 PM

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i dont knowwhat that means.

trim sage Jul 18, 2025, 8:23 PM

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Let a be 1000 dollars and b the interest + 100%

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So a = 1000 dollars and b = 103.4%

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The deposit a dollars every month and the interest is added so times b

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The first quarter would be a * b

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The second would be a*b plus 1000 dollars and increased by the interest

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So (a*b+a)*b

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The third quarter would be that increased by 1000 dollars and the interest

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((ab+a)b+a)b

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And it would go like this

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First quarter: ab

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Second quarter: (ab+a)b so ab²+ab

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Third quarter: ((ab+a)b+a)b so ab³+ab²+ab

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Do you see the pattern

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It's a geometric series without the first term: a+ar+ar²+ar³+ar⁴+…

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You there? @vivid ledge

edgy crag Jul 19, 2025, 7:54 PM

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3.4% interest means 3.4% per year. The compounding period is when the interest is paid.

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That means it's 3.4%/4 per quarter.

#help