My Math Forum Compounding Formula Needed?

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 October 10th, 2012, 07:03 PM #1 Newbie   Joined: Oct 2012 Posts: 3 Thanks: 0 Compounding Formula Needed? Hello all! I am a sales professional giving a big presentation next week and in preparation for a lecture on sales performance I need a formula to solve the following issue: My stores offer a credit card. Every time a customer signs up for a credit card, they spend an average of $4.00 per day more in sales than a non credit card holding customer throughout the course of the year. My store has a goal of 10 credit card sign ups every day, but it is currently at a year to date trend of 4.5 credit sign ups per day. 283 days have passed in the year so far, and I would like to know that formula would be used to determine the amount of lost sales so far for the year being at 4.5 credit signups per day vs if they had been at 10 every day throughout the year. I also need to determine how many sales dollars they would pick up at 10 signups a day (vs their current trend of 4.5) every day for the rest of the year (82). I'm desperate for help, and highly appreciate anyone who can take the time to do so. Thanks! October 10th, 2012, 08:17 PM #2 Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Compounding Formula Needed? Quote:  Originally Posted by RUXXIAN Hello all! 283 days have passed in the year so far, and I would like to know that formula would be used to determine the amount of lost sales so far for the year being at 4.5 credit signups per day vs if they had been at 10 every day throughout the year. The Lost Sales=$4×(10-4.5)credit cards×283 days?

October 10th, 2012, 10:56 PM   #3
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Quote:
 Originally Posted by RUXXIAN 283 days have passed in the year so far, and . . . I also need to determine how many sales dollars they would pick up at 10 signups a day (vs their current trend of 4.5) every day for the rest of the year (82).
Clearly, the difference in sales based on 10 sign-ups vs 4.5 sign-ups is (10 - 4.5) × $4 per day, which is$22 per day whether you are talking about the past or the future. What puzzles me is why you think the current year has 283 + 82 = 365 days. There are 366 days in 2012, as it's a leap year, right? That's 284 that have gone already (up to the 10th of October) and another 82 to go.

October 10th, 2012, 11:01 PM   #4
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Quote:
 Originally Posted by skipjack There are 366 days in 2012, as it's a leap year, right?
Right, miserable day plus.

October 11th, 2012, 05:14 AM   #5
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Re: Compounding Formula Needed?

Quote:
Originally Posted by stainburg
Quote:
 Originally Posted by RUXXIAN Hello all! 283 days have passed in the year so far, and I would like to know that formula would be used to determine the amount of lost sales so far for the year being at 4.5 credit signups per day vs if they had been at 10 every day throughout the year.
The Lost Sales=$4×(10-4.5)credit cards×283 days? But it is a miss of 5.5 sign ups per day at$4 per sign up per day compounding, right?

Meaning on day 1 of the year it's 5.5 missed sign ups x $4 + day 2 at 11 missed sign ups x$4 daily spend + day 3 at 16.5 lost sign ups x $4 daily spend, etc. Thanks for your help.  October 11th, 2012, 05:49 AM #6 Global Moderator Joined: Dec 2006 Posts: 19,045 Thanks: 1618 Yes, you need to total the numbers of days. For the first 284 days, the total is 1 + 2 + 3 + . . . + 284. To evaluate such a total, use the formula 1 + 2 + . . . + n = n(n + 1)/2. Just evaluate that formula for n = 284 and for n = 82, then multiply the results by$22. Note that the sign-ups already missed will continue to cause lost sales indefinitely.
 October 11th, 2012, 08:05 AM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,594 Thanks: 843 Re: Compounding Formula Needed? If you wanna "see" it, do one week: DAY1 : 7 : 154 (7 * 22) DAY2 : 6 : 132 DAY3 : 5 : 110 DAY4 : 4 : 088 DAY5 : 3 : 066 DAY6 : 2 : 044 DAY7 : 1 : 022 ============ TOTAL....616 n = 7 n(n + 1)/2 * 22 = 7(/2 * 22 = 28 * 22 = 616 NOTE that sum 1 to 7 = 28. If you want a formula to handle changes to present stats: t = target (now 10) a = actual (now 4.5) e = extra spent (now 4) n = number of days (whatever) Formula: [n(n + 1) / 2] * [e(t - a)] QUESTION: if I get a card from you but spend $2 less, will you sue me? October 11th, 2012, 02:27 PM #8 Newbie Joined: Oct 2012 Posts: 3 Thanks: 0 Re: Compounding Formula Needed? Quote:  Originally Posted by Denis If you wanna "see" it, do one week: DAY1 : 7 : 154 (7 * 22) DAY2 : 6 : 132 DAY3 : 5 : 110 DAY4 : 4 : 088 DAY5 : 3 : 066 DAY6 : 2 : 044 DAY7 : 1 : 022 ============ TOTAL....616 n = 7 n(n + 1)/2 * 22 = 7(/2 * 22 = 28 * 22 = 616 NOTE that sum 1 to 7 = 28. If you want a formula to handle changes to present stats: t = target (now 10) a = actual (now 4.5) e = extra spent (now 4) n = number of days (whatever) Formula: [n(n + 1) / 2] * [e(t - a)] QUESTION: if I get a card from you but spend$2 less, will you sue me?
No, I will not sue you : P

One last question to make sure I am perfectly clear (because I can't afford to have the wrong formula for my spreadsheet due to not explaining it correctly), this is what I am looking at:

Using fictional numbers to represent one of my stores:

A Credit customer spends an average of $2,300 more per year than a non credit member. The store is averaging 4.5 credit sign ups per day, against a goal of 10 sign ups per day. I am seeking to solve the amount of lost money (based on the average spend) through today (day #284). 2300/365 gives me an average daily spend of$6.30 per day, per credit sign up.

Using the formula above:

$6.30 (average spend) x 5.5 (average lost credit signup) =$34.65 per day compounding.

n(n + 1)/2 * 34.65

284(284+1)/2 * 34.64 = $1,407,223.13 lost dollars in sales, correct?  October 11th, 2012, 03:07 PM #9 Global Moderator Joined: Dec 2006 Posts: 19,045 Thanks: 1618 The last line should have been 284(284+1)/2 * 34.65 =$1,402,285.5. If the annual spend of $2,300 is accurate to, say, 4 significant figures, your calculated amount of$1,402,285.5 might as well also be rounded to 4 significant figures.
 October 12th, 2012, 06:35 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,594 Thanks: 843 Re: Compounding Formula Needed? Well, if it was me doing this, I'd round the 34.65 to 34 or 35. This kind of estimate is just that, an estimate; plus it is usual for whoever does such a presentation to end with: even if I'm 20% short or 20% over, it means the 1 point 4 million translates to anywhere from 1 point 12 million to 1 point 68 million... get my drift?

 Tags compounding, formula, needed

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