Factor Payment Help

canehdien
canehdien used Ask the Experts™
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User enters:
Total invoice to be factored: __________
Pay twice a month Day1: ___  Day2: ____
OR
Pay once a month Day: ___
First Payment from Client Due: __ __ __
Total number of payments: ____
Amount of each Payment: _____

I need to know:
50% factor payment up front: _____
Less EAS Factor Fee: ______ (interest rate 3.33% monthly)
Transfer amount: ____ (50% factor payment minus the EAS Factor fee)
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This looks like a miserable compound interest problem. Some clarifications needed here

(1)Total invoice to be factored = amount owed by client ?

(2) Is the interest is 3.33% on  the amount owed, is so is this compounded monthly for monthly payments and semi-monthly for 2 payments per month

(3) I have no idea what these mean

50% factor payment up front: _____
Less EAS Factor Fee: ______ (interest rate 3.33% monthly)
Transfer amount: ____ (50% factor payment minus the EAS Factor fee)

ie what does  EAS stand for.


      I am not sure your problem has been described presciely enough for us Maths types. Once defined I can solve just about any actuarial problem there is.

Regards

GfW

Author

Commented:
(1) - yes, amount owed by client
(2) - interest is based on the unpaid amount - compunded monthly
(3) -
$2000 invoice to factor      
Clients pays $250 x 8 months= $2000  
Amount to be Factor 50%=$1000  
Schedule of Payments and Interest:
   
Month Monthly Payment Remaining Amount Owed Principal Paid Interest Paid Cumulative Interest Paid  
0           0           883                               0                                      0                                          0  
1          125        783                            99                                     26                                        26  
2           125       681                           102                                   23                                         50  
3          125         576                          105                                   20                                            70  
4           125         467                         108                                   17                                            87  
5          125        355                           111                                 14                                         101  
6          125         240                          115                                    10                                         112  
7         125           122                         118                                   7                                            119  
8         125           0                            122                                   3                                             123  
 
            1000                                     880                                120                                             2000
I am not understanding the problem.  Is  this it?

Client owes $2000 but since he pays $1000 up front he infact now owes $1000, he wants to pay $125 each month for 8 payments (since he now owes only $1000 the payments are $125). However because of interest he must pay down a little more than $1000 so that after his 8 payments all will have been payed exactly . In this case he must come up with another $117 so he owes $883 at the beginning of the first month.

  The question becomes how much he actually owe at the begining of the payments for his declared schedule of payments to exactly cover the whole amount + the interest.

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If you pay Payment each month for n months then for this to exactly match Total when paying 3.33% interest monthly the formula for Total is

  Total = Payment*(1.0333^(n +1) - 1 )/( 1.033*(1.033-1) )

so for n = 8 and Payment = 125 the initial amount owed is $935.4001 which does not corresspond with your $883, .... Hmm?  Looking at your table I get the first month's interest as $29.4

Anyway this will get the ball rolling on this post.

GfW

oops, few errors just above let me rework it, (I am rushing) .

the formula is

 Total = Payment*(1.0333^n   -  1 )/( 0.033*1.033^n )

which give an initial total amount of 865.37  fo  n = 8 and Payment = 125
Is this getting us some where? If so I will carry on.
I ran the following Javascript, (just put into a .htm and open it in a browser)
<script>
sp='....................'
NumWeeks=8
Pymnt=125
IntPayed=0
Ipow = Math.pow(1.0333,NumWeeks)
Total = Pymnt*(Ipow   -  1 )/( 0.0333*Ipow )
document.write('Initial Total =$',Total, ' Payment=',Pymnt, ' Number of weeks=',NumWeeks,'<br>')
document.write('Month' ,sp,'Total left',sp,sp,'Interest payed<br><br>')
for (i=1;i<=8;i++){
Total=Total+0.0333*Total - Pymnt
IntPayed=IntPayed + 0.0333*Total
document.write(i,'. ',sp ,Total,sp, IntPayed,'<br>')
}
</script>

and got the following

Initial Total =$865.3736524053306 Payment=125 Number of weeks=8

Month....................Total left........................................Interest payed
1. ....................769.1905950304282....................25.614046814513262
2. ....................669.8046418449414....................47.918541387949816
3. ....................567.109136418378....................66.80327563068181
4. ....................460.9938706611099....................82.15437152369676
5. ....................351.3449665541249....................93.85415890994912
6. ....................238.04475394037723....................101.78104921616368
7. ....................120.97164424659181....................105.80940496957518
8. ....................3.311129148642067e-12....................105.8094049695753
Damn I got the interest calc mixed up in the loop, the 2 lines should be in this order

IntPayed=IntPayed + 0.0333*Total
Total=Total+0.0333*Total - Pymnt

Giving

Initial Total =$865.3736524053306 Paynment=125 Number of weeks=8

month....................Total left........................................interest payed
1. ....................769.1905950304282....................28.816942625097514
2. ....................669.8046418449414....................54.43098943961078
3. ....................567.109136418378....................76.73548401304732
4. ....................460.9938706611099....................95.62021825577932
5. ....................351.3449665541249....................110.97131414879428
6. ....................238.04475394037723....................122.67110153504663
7. ....................120.97164424659181....................130.5979918412612
8. ....................3.311129148642067e-12....................134.62634759467272

All of this is easily ajusted for semi-monthly payments
Sorry where I have weeks I mean months in all the above
Thanks for the points. GfW

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