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Thread: Need Help Solving a Word Problem Involving Fundraising and Compound Growth Please!

  1. #1

    Need Help Solving a Word Problem Involving Fundraising and Compound Growth Please!

    A leader in a non-profit organization recently challenged us to realize the potential outcome of setting regular new support goals. His query to us was to determine how much money you could raise at the end of one year, if every three days you gained a new $25 per month supporter.

    Is there a formula for this that could be used to demonstrate $50 or $100 as well?
    Each new supporter is a monthly contributor, so the first ten or so would obviously equate to $300 at the end of a year, correct? ($25*12)
    However, as you gain a new supporter every 3 days, the last new supporter would only bring $25 in for that year.

    What formula could demonstrate how to express this math, in the simplest format, as well as the most versatile- meaning where the period of days (3) could be set to once a week (7), for instance. The goal period will remain one year for this exercise.

    Thank you for any help you can give. I tried to chart this on Excel and got very overwhelmed!
    rcaseytx

  2. #2
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by rcaseytx View Post
    Each new supporter is a monthly contributor, so the first ten or so would obviously equate to $300 at the end of a year, correct? ($25*12)
    No.

    $300 is what one contributor would have given, after donating $25 in each of 12 months.

    Ten new contributors donating $25/month for 12 months would be:

    10 * $25 * 12 = $3,000

    Your task seems like a summation. Let's assume 10 new contributors each month. The revenue stream is a pattern that looks like this:

    JAN 10*25*12
    FEB 10*25*11
    MAR 10*25*10
    APR 10*25*09
    MAY 10*25*08
    JUN 10*25*07
    JUL 10*25*06
    AUG 10*25*05
    SEP 10*25*04
    OCT 10*25*03
    NOV 10*25*02
    DEC 10*25*01

    Tell Excel to add 'em up.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
    Quote Originally Posted by mmm4444bot View Post
    No.

    $300 is what one contributor would have given, after donating $25 in each of 12 months.

    Ten new contributors donating $25/month for 12 months would be:

    10 * $25 * 12 = $3,000

    Your task seems like a summation. Let's assume 10 new contributors each month. The revenue stream is a pattern that looks like this:

    JAN 10*25*12
    FEB 10*25*11
    MAR 10*25*10
    APR 10*25*09
    MAY 10*25*08
    JUN 10*25*07
    JUL 10*25*06
    AUG 10*25*05
    SEP 10*25*04
    OCT 10*25*03
    NOV 10*25*02
    DEC 10*25*01

    Tell Excel to add 'em up.
    Very nice- I'll give it a go- thank you.

  4. #4
    Quote Originally Posted by mmm4444bot View Post
    No.

    $300 is what one contributor would have given, after donating $25 in each of 12 months.

    Ten new contributors donating $25/month for 12 months would be:

    10 * $25 * 12 = $3,000

    Your task seems like a summation. Let's assume 10 new contributors each month. The revenue stream is a pattern that looks like this:

    JAN 10*25*12
    FEB 10*25*11
    MAR 10*25*10
    APR 10*25*09
    MAY 10*25*08
    JUN 10*25*07
    JUL 10*25*06
    AUG 10*25*05
    SEP 10*25*04
    OCT 10*25*03
    NOV 10*25*02
    DEC 10*25*01

    Tell Excel to add 'em up.
    Also- another math forum solved it by stating that you could just multiply the gift amount (as long as it stayed the same) by the number 78. sounds simple but their explanation was pretty complicated. Any thoughts on that approach?

  5. #5
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by rcaseytx View Post
    Also- another math forum solved it by stating that you could just multiply the gift amount (as long as it stayed the same) by the number 78
    If we multiplied by 780 (that is, 10 times 78), then it would give the same result as totaling the dollar amounts in the pattern I had previously posted.

    This is because 1+2+3+4+5+6+7+8+9+11+12 equals 78.

    We could factor out (10*$25) from each quantity being added. In other words:

    10*$25*12 + 10*$25*11 + 10*$25*10 + + 10*$25*3 + 10*$25*2 + 10*25*1

    is the same as:

    (10*$25)*(12+11+10+9+8+7+6+5+4+3+2+1)

    (10*$25)*(78)

    It would not work, if you chose a different period (eg: one new contributor every three days, five new contributors every week). You could still factor, but the (new) related values would add up to something other than 78.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  6. #6

    Thank you!

    Quote Originally Posted by mmm4444bot View Post
    If we multiplied by 780 (that is, 10 times 78), then it would give the same result as totaling the dollar amounts in the pattern I had previously posted.

    This is because 1+2+3+4+5+6+7+8+9+11+12 equals 78.

    We could factor out (10*$25) from each quantity being added. In other words:

    10*$25*12 + 10*$25*11 + 10*$25*10 + + 10*$25*3 + 10*$25*2 + 10*25*1

    is the same as:

    (10*$25)*(12+11+10+9+8+7+6+5+4+3+2+1)

    (10*$25)*(78)

    It would not work, if you chose a different period (eg: one new contributor every three days, five new contributors every week). You could still factor, but the (new) related values would add up to something other than 78.
    Thank you! Genius!

  7. #7
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by rcaseytx View Post
    Genius!
    Also known as Algebra!
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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