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Math Help - Term deposit interest calculation.

  1. #1
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    Term deposit interest calculation.

    Hi,

    I've been struggling with this problem for days now. It seems really simple, but I'm having issues. Here's the problem:

    Bob gets paid fortnightly. He wants to save 6000 dollars in 1 year. His savings account offers 5 percent interest for 3 months maturity with a minimum of $2000 term deposit. Bob currently has no savings.

    (i) If he starts on the 1/1/10, how much must he save fortnightly to reach his target by the 31/12/10? Provided that he deposits the same amount every fortnight and ends up with $6000 at the end of the year.

    Any pointers on how to approach this or (even preferably) worked solutions would be very much appreciated.

    Thank you so much
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  2. #2
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    Re: Term deposit interest calculation.

    Quote Originally Posted by kkevv View Post
    Hi,

    I've been struggling with this problem for days now. It seems really simple, but I'm having issues. Here's the problem:

    Bob gets paid fortnightly. He wants to save 6000 dollars in 1 year. His savings account offers 5 percent interest for 3 months maturity with a minimum of \$2000 term deposit. Bob currently has no savings.

    (i) If he starts on the 1/1/10, how much must he save fortnightly to reach his target by the 31/12/10? Provided that he deposits the same amount every fortnight and ends up with $6000 at the end of the year.

    Any pointers on how to approach this or (even preferably) worked solutions would be very much appreciated.

    Thank you so much
    editted to correct \$ signs
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  3. #3
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    Re: Term deposit interest calculation.

    Quote Originally Posted by kkevv View Post
    Hi,

    I've been struggling with this problem for days now. It seems really simple, but I'm having issues. Here's the problem:

    Bob gets paid fortnightly. He wants to save 6000 dollars in 1 year. His savings account offers 5 percent interest for 3 months maturity with a minimum of \$2000 term deposit. Bob currently has no savings.

    (i) If he starts on the 1/1/10, how much must he save fortnightly to reach his target by the 31/12/10? Provided that he deposits the same amount every fortnight and ends up with $6000 at the end of the year.

    Any pointers on how to approach this or (even preferably) worked solutions would be very much appreciated.

    Thank you so much
    .
    The problem is very badly specified. Have you given it exactly and completely?

    Some of the problems.

    What is the relevance of term deposits? In standard terminology of US banking, a term deposit is a deposit withdrawable without penalty only after a predetermined and fixed period, the term. For many types of term deposit, only a single deposit is permitted into an account.

    In US banking, deposits into savings accounts are legally term deposits but are in practice withdrawable on demand, and they always permit multiple deposits into an account.

    The rules for when interest begins to accrue differ among US banks; there is no standard. Probably most common is accrual starts on the day of deposit. Is that specified?

    Does interest accrue only when the aggregate balance reaches \$2500 but then accrues interest on the entire balance?

    Are deposits by fortnight or twice a month? In the one case, we are talking about 26 deposits; in the other, we are talking about 24.

    Without knowing those things, I can't be sure my interpretation is correct.

    x = the amount of the bi-monthly deposit. The calculations become much harder if deposits are made every fourteen days. I'm too lazy to touch it.

    i = relevant interest rate.

    t = the deposit when interest begins to accrue.

    $Equation\ 1:\ t = ceiling \left(\dfrac{2500}{x} \right).$

    $Equation\ 2:\ i = \dfrac{0.05}{24}.$

    $Equation\ 3a:\ t = 24 \implies x = \dfrac{6000}{24}.$

    $Equation\ 3b:\ t < 24 \implies 6000 = tx(1 + i)^{(24 - t)} + x\left(\dfrac{(1 + i)^{(23-t)} - 1}{i}\right).$

    Now equation 3 looks as though it has two unknowns, but t is dependent on x so it really has only one unknown. I doubt there is any closed form solution. Because t can take on only a small number of values, you can solve equation 3 for x given each possible value of t and find which satisfies equation 1.

    What kind of course gave you this mess of a problem, anyway?
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  4. #4
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    Re: Term deposit interest calculation.

    Equation 3b should be $6000 = tx(1 + i)^{(24 - t)} + x\left(\dfrac{(1 + i)^{(24 - t)} - 1}{i}\right).$
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  5. #5
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    Re: Term deposit interest calculation.

    By the way, I assumed semi-monthly compounding, which is seldom found in practice. Furthermore, because of truncation and rounding issues, you will not get an exact result. When I worked this out using my assumptions I was off by 10 cents. If the regular deposit is adjusted by 1 cent each deposit, the answer would be off by 14 cents the other direction. You are very unlikely to get an exact answer.

    I still think whoever designed this problem is bonkers.
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  6. #6
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    Re: Term deposit interest calculation.

    Thanks for your help, Jeff. I presented the problem as it was given to me. It was my tutor who gave it to me and I think there may be an issue with it.

    Thank you for your input; I'm pretty sure I would have struggled for a few more hours with it if not for your help.
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  7. #7
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    Re: Term deposit interest calculation.

    Quote Originally Posted by JeffM View Post
    By the way, I assumed semi-monthly compounding, which is seldom found in practice.
    Agree with you on that Sir JeffM.
    More unusual (and preposterous/hilarious) perhaps is 365.25 days compounding as indicated here. Laughed for hours on that one.
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