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Beautifulgirl17 Group Title

Gabby starts to save at age 20 for an extended vacation around the world that she will take on her 40th birthday. She will contribute $250 four times each year to the account, which earns 1.55% annual interest, compounded annually. What is the future value of this investment when she takes her trip?

  • 2 years ago
  • 2 years ago

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  1. Beautifulgirl17 Group Title
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    I've used the future value formula, found the yrs to be 20, but ponder whether the present value is 1000 from (250*4) or if that is calculated into the 20yrs previous to the power enhancement? Please help. Thankx :3

    • 2 years ago
  2. Cryptic57 Group Title
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    I shouldn't do this, I should show you how to do it but I'm heading off so $23,394.10. I've added the amounts at the end of the compounding period, ie start with 0. As I'm in a hurry best get someone to check this.

    • 2 years ago
  3. jennyang87 Group Title
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    Sure thing. \[\sum_{n=1}^{20}1000(1.0155)^{n}\] If you plug this in to the excel, you should see the amount below.

    • 2 years ago
  4. EdwardDeR Group Title
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    $23,394 is approximately right but, depending how close you look at the problem, maybe not quite right. It comes from =FV(rate, nperiods, pmt, pv, type) It comes from =FV( (1.55%/4), (20*4), 250, 0, 0) This is a tricky problem. Here's why the above is not exact: - Cryptic is compounding the amount quarterly, (at 1/4 the rate), not annually - Cryptic is using an "end of period" payment. My read of the question is, use a "start of period" payment. So here's how I would do it, it would require 2 steps. First, how much is it worth if Gabby saves $250 a quarter for 1 year, with interest paid at the end of the year? (savings put at the start of the year). You do this in the spreadsheet, 250 every quarter, work out the quarter's interest (at 1.55% / 4), but don't credit the interest until the end of the year. interest is $9.6875. You try. Second, we can now use the =FV() formula, with 20 periods (which is correct, not 80 periods), because the interest is compounded _annually_ not quarterly. my answer: = FV(annu_rate, nperiods, annual_pmt, pv, type) my answer: = FV(1.55%, 20, $1009.6875, 0, 0) = $23,462.97 why have I put 0 (end of period) in the type? because I used the future value of 4 quarterly payments of $250, i.e. how much they are worth at the _end_ of the year, not their PV. You should get the same result if you do a table of 80 payments in a list in excel (remember to credit the interest at the end of 4 periods, not each row). That's just my opinion, but maybe I over-analysed the question.

    • 2 years ago
  5. EdwardDeR Group Title
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    And just to give some feedback on Jennyang spreadsheet: the problems I have with it are 1) you've counted 21 lots of $1000, but my interpretation of the question is 20 lots of $1000. 2) you're crediting interest just the same as for 1 bullet payment of $1000 each year, you don't give credit for 9 months interest on part the balance, 6 months interest on part the balance and 3 months interest on part the balance.

    • 2 years ago
  6. TheBonc Group Title
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    23,237.86

    • one year ago
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