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Calculating billing period

  • 31-01-2012 9:55pm
    #1
    Moderators, Education Moderators, Technology & Internet Moderators, Regional South East Moderators Posts: 24,056 Mod ✭✭✭✭


    Okay. I need a fresh pair of eyes to look over a billing question. I think this forum is best suited, as its a maths related question. I'm trying to calculate an electricity period over a period of days but when I add up each persons total, it exceeds the actual bills total. So clearly I am messing up somewhere, but a fresh pair of eyes may spot my problem quicker.
    ELECTRICITY
    01/11/2011-11/01/2012
    63.02 for 71 days
    1.13 per day.

    Person A – 01/11/2011 – 09/11/2011 (Three tenants in the house)
    Person B – 01/11/2011 – 14/12/2011 (Two Tenants in the house)
    Person C – 01/11/2011 – 11/01/2012 (One tenant in the house)

    Person A was present for 9 days of the billing period. At a cost of 1.13 per day, the total is 10.17. Divided by 3 tenants, her total is only 3.39.
    Person B was present for 64 days of the billing period. She already paid for 9 days, bringing her total billing period to 55 days. At a cost of 1.13 per day, she owes 62.15c. Divided between the two tenants, her total is 31.07.
    Person C was present for all 71 days of the billing period. She already paid for 55 days. Her billing period remaining is 16 days (71 – 55 = 16 days unbilled. But, 01/11/11 – 11/01/12 is 28 days?). At a cost of 1.13 per day, she owes €18.08.

    In total, for the Electricity;
    Person A owes just €3.39.
    Person B owes €31.07 + €3.39. (if her billing period is 55 days unpaid, 64-9=55 days)
    Person C owes €18.08 + €31.07 + €3.39 (if her billing period is 16 days, as in earlier paragraph)

    Person A owes just €3.39.
    Person B owes €19.77 + €3.39 = €23.16 (if her billing period is 35 days unpaid, which is Nov 09 – Dec 14th)
    Person C owes €19.77 + €31.64. (if basing her period at 28 days unpaid)

    So you will see both attempts at my calculations are doing;
    1) Never giving me the exact billing total when adding each persons bill.
    2) I'm getting conflict unpaid periods depending how I calculate it.

    So please, before I go insane, can someone give me a helping hand and point out my mistake? Iv been at this the past few weeks, the tenants wish to pay by the day they left and not the week ending (which I can provide accurate calculations for). I cant seem to get it adding up, person B provided calculations that exceeded the total by over a hundred euro and person A doesn't seem to care as she will only pay her calculation.

    Bah humbug! Please help! :)


Comments

  • Registered Users, Registered Users 2 Posts: 1,163 ✭✭✭hivizman


    Several points to raise.

    First, if the bill runs from 1 Nov. 2011 to 11 Jan. 2012, are the first and last days included? If both days are included, then there are actually 72 days in the period (30 days in November, 31 days in December and 11 days in January).

    Secondly, you divided the total cost of 63.02 into the number of days, but you should have divided the total cost by the number of days. Assuming 72 days in total, the cost per day is actually 0.875.

    The two obvious ways of allocating the cost are:

    1. Split the cost per day equally among the tenants present on any given day.

    2. Assume that the cost per day actually varies according to the number of tenants in place on any day (more tenants will lead to greater use of electricity).

    Tenant A is there from 1 Nov. 2011 to 9 Nov. 2011, so including first and last days, A is there for 9 days.

    Tenant B is there from 1 Nov. 2011 to 14 Dec. 2012, so including first and last days, B is there for 30 + 14 = 44 days.

    Tenant C is there for the full 72 days.

    So, there are 9 + 44 + 72 = 125 "tenant days", and the cost per tenant day is 63.02/125 = 0.504.

    On the first basis, we have the following:

    Tenant A: 9 days at 0.875/3 per day = 2.65

    Tenant B: 9 days at 0.875/3 per day + 35 days at 0.875/2 per day = 17.94

    Tenant C: 9 days at 0.875/3 per day + 35 days at 0.875/2 per day + 28 days at 0.875 per day = 42.43

    Total 2.65 + 17.94 + 42.43 = 63.02.

    On the second basis, we have the following:

    Tenant A: 9 "tenant days" at 0.504 per day = 4.54
    Tenant B: 44 "tenant days" at 0.504 per day = 22.18
    Tenant C: 72 "tenant days" at 0.504 per day = 36.30

    Total 4.54 + 22.18 +36.30 = 63.02.

    I hope this helps - if I were a professional accountant, I'd be sending you a bill for 100 euro for my time!


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