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Math Help - Weekly interest rate applied to four-weekly deposits

  1. #1
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    Weekly interest rate applied to four-weekly deposits

    Here is what I have to do, given a weekly interest rate of 2%

    Initial deposit is $1000
    Four-weekly start of the period deposits of $100 for 13 periods
    Finding the future value of these amounts

    Here is what I tried

    Making the interest rate from weekly to four-weekly
    =(1+0.02)^4-1
    =(1.02)^4-1
    =1.08243216-1
    RATE=0.08243216

    FV = PV x FVIF(i%,n) + PMT x FVIFAD(i%,n)

    FV = PV(1+i)^N + PMT(1+i)[{(1+i)^N}-1]/i

    FV = 1000(1+0.08243216)^13 + 100(1+0.08243216)[{(1+0.08243216)^13}-1]/0.08243216

    FV = 1000(1.08243216)^13 + 100(1.08243216)[{(1.08243216)^13}-1]/0.08243216
    FV = 1000(2.8003281854481790518074084843015) + 100(1.08243216)[{2.8003281854481790518074084843015}-1]/0.08243216

    FV = 2800.33 + 108.24[1.8003281854481790518074084843015]/0.08243216

    FV = 2800.33 + 108.24[21.840119019666342017574311825639]
    FV = 2800.33 + 2363.97
    FV = $5164.30

    Have I done this right.
    Last edited by dexteronline; August 27th 2011 at 04:57 AM. Reason: was asked to simplify the formula by TKHunny
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  2. #2
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    Re: Weekly interest rate applied to four-weekly deposits

    Hard to say. Does the problem statement say WHEN to find the future value?

    Other than that, it looks pretty good. Kind of a mess, though. You may widh to consider some notation simplification.
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  3. #3
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by TKHunny View Post
    Hard to say. Does the problem statement say WHEN to find the future value?

    Other than that, it looks pretty good. Kind of a mess, though. You may widh to consider some notation simplification.
    I am developing a savings calculator for someone
    At first his requirements included finding the future value (ending balance) given there is an initial deposit for example $1000 followed by weekly deposits of say $100 for a year. The interest rate is weekly

    I showed him my work and my results matched with his own calculations

    then he asked me to amend the calculator so that there be an initial deposit of say $1000 followed by monthly deposits (not actually monthly but four-weekly deposits thus to make up the 13 periods in a year). the interest rate is still weekly

    When I showed him my calculations, it differed from what his calculations were showing

    I have asked him to show me his own calculations so to see why the results differ
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    Re: Weekly interest rate applied to four-weekly deposits

    Code:
    0(0)  1000.00   100.00                  1100.00
     
    1(4)            100.00       90.68      1290.68
     
    2(8)            100.00      106.39      1497.07
     
    3(12)           100.00      123.41      1720.48
     
    .....
     
    11(44)          100.00      321.02      4315.36 **
     
    12(48)          100.00      355.72      4771.08 **
     
    13(52)             .00      393.29      5164.37
    Your results are correct: looks like what I show above.

    ** Example of period to period calculation: 4315.36(1.02^4) + 100 = 4771.08

    OF COURSE, I prefer MY formula to yours(!):
    A = 1000
    P = 100
    n = 13
    i = 1.02^4 - 1

    F = (A + P)[(1 + i)^n] + P[(1 + i)^n - 1]/i - P ; substitute above:
    F = 5164.3729059596311476.....

    Can be a bit simplified to:
    F = [Aki + P(ki + k - i - 1)] / i where k = (1+i)^n
    Last edited by Wilmer; August 27th 2011 at 07:54 AM. Reason: Add the "Wilmer Formula!"
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    Re: Weekly interest rate applied to four-weekly deposits

    You still must specify WHEN. Assuming one period past the last deposit is common, but not assured.
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by TKHunny View Post
    You still must specify WHEN. Assuming one period past the last deposit is common, but not assured.
    I think the client needed to find the balance on the last day of the year on may be a day after the last day of the year

    He finally agreed to my calculations
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by dexteronline View Post
    I think the client needed to find
    Exactly my point. You're guessing. In this case, you had a separate verification. Good luck with that.
    Last edited by TKHunny; August 27th 2011 at 06:11 PM.
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by TKHunny View Post
    Exactly my point. Your guessing. In this case, you had a separate verification. Good luck with that.
    @TKHunny

    Did I screw up the whole thing?

    I know in your last post you did point me in right direction yet I am not that smart neither am I aware of the intricacies of how savings accounts function.

    So what is that I should have asked him or what is that I should have known before making these calculations
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by dexteronline View Post
    I think the client needed to find the balance on the last day of the year on may be a day after the last day of the year
    What are you two talking about?

    This is a straightforward financial problem, with an initial deposit, regular periodic deposits
    at the START of the periods, and a regular periodic rate.

    No need to worry about anything else; like, we don't worry (say on a regular savings account
    with monthly deposits) about the balance after 9 months and 3 weeks...sure, it's something
    that can be calculated, but is not part of the regular financial formula.

    Here, 5164.37 = balance after 13 periods is the answer; over and out!
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    Re: Weekly interest rate applied to four-weekly deposits

    Respectfully disagree. The problem statement should say "when". It is required in the real world.
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by TKHunny View Post
    Respectfully disagree. The problem statement should say "when". It is required in the real world.
    Respectfully agree IF this was "real world"...
    Respectfully disagree that it is; here is the problem EXACTLY as initially posed by Dexter:

    > Here is what I have to do, given a weekly interest rate of 2%
    > Initial deposit is $1000
    > Four-weekly start of the period deposits of $100 for 13 periods
    > Finding the future value of these amounts

    The answer to that is the straight-forward formula, nothing else....
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    Re: Weekly interest rate applied to four-weekly deposits

    Respectfully continue to disagree.

    The "13 periods" refers only to the payments, not necessarily to the future time when the FV is requested. It COULD. DOES it? It is a poorly written question.

    I never use formulas, anyway. I would be more curious about the actual requested time than pathological formula users. I suppose this also would fix the problem statement. "Here is the formula you should use." or "Please describe any assumptions you made in reaching your solution."
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  13. #13
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    Re: Weekly interest rate applied to four-weekly deposits

    This conversation reminds me of what transpired when I started out developing Visual Calculus Applets in 2007. Then not knowing that posting links on newsgroups is considered SPAM, I was told off by the pundits on newsgroups such as for Java programming. Those on such newsgroups who considered themselves as final authority on subject matter wasted no time in lampooning my posts and calling an ignorant, stupid coder

    I agree that I am not well versed in English even though I did attend a college in NY for 6 years (I guess you can lay the blame on college for not educating me as they were suppose to) but the point is most problems I read about finding future value of annuities simply state the periodic deposit amount(PMT) for a number of periods (NPER), an initial deposit amount(PV) and an interest rate usually quoted per year and sometimes compounded multiple times within a year. All these problems simply state to find the future value of the sums, or amounts.

    Now having said that, I never worked as an accountant or financial analysts in real life so I can't comment what constraints would be given that you have to consider while tackling these problems

    As for myself, I sold off my Visual Calculus Applets (24 of them) for a mere sum of $600, the reason for disposing those valuable tools has to do with the lack of visitors to the site and refusal from major math directories including Mathematical Association of America's to list my tools. Since then I have concentrated on learning financial mathematics by researching the topics and creating online and Windows based finanicial calculators and financial calculation tools. And my work has been appreciated by college students who need to solve such problems for their coursework and also by professional finanical analysts who use these tools to do number crunching. May be I am stupid but somehow my programmed calculators provide accurate results
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    Re: Weekly interest rate applied to four-weekly deposits

    I tend to agree. Given a formula and the values to populate the parameters, it is exactly as I have stated it. Perhaps this reference was in the problem section or listed as an assumption in the section readings.

    Given the ENTIRE problem, there MUST be some way to know WHEN the value is desired. In the problem statement you provided, it just isn't there. It is certainly an easy assumption, but it may not be assumed to be the only possible solution to the problem as stated. I know I would provide additional answers if I were given the chance on an exam and I would argue their validity to the highest possible authority. As stated, anything after month 13 should be accepted as a correct answer.

    My views. I welcome others'. And I yield, having stated my views quite clearly and sufficiently.
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    Re: Weekly interest rate applied to four-weekly deposits

    Quote Originally Posted by dexteronline View Post
    Maybe I am stupid but somehow my programmed calculators provide accurate results
    Dexter, as I said on another thread, you are to be admired;
    plus I assure you that no one here thinks you're stupid;
    you also have a high IQ (Imagination Quotient!): you've somehow imagined that...
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