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PROM® 520A APRChecker PC & Dealer Reserve
Sample Dealer Reserve Calculations

This page illustrates dealer reserve calculations using the PROM 520A APR Checker & Dealer Reserve PC Program.

Example #1 - No Odd Days

Example #2 - With Odd Days


Example #1 - No Odd Days

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This is a straight-forward installment loan with exactly 1 month to the first payment.  The loan interest rate is 11.25%, and the bank "buy" rate is 8.90% with the bank paying 75% of the calculated dealer reserve.

The dealer reserve is calculated by the "Difference in Charges" method, which is the most common.  We have specified the Federal Calendar to measure the first period to make sure that it is exactly one month long.

 


Input dialog showing entered values


Output window showing results

Calculation methods
for Example #1

 

 

 

 

 

 

 

 

 

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There are several steps required to reach the final result of the dealer reserve and advance.  Note that in keeping with proper mathematical rules, no rounding is done on intermediate calculations: only the final result is rounded.

In the difference-in-charges method, a second, hypothetical loan is calculated using the lender's "buy" rate of 8.90%.  The finance charge on this hypothetical loan is the amount that the lender would retain if 100% of the dealer reserve were paid to the dealer (see below).

The purpose of calculating the lender's retention first is to make sure the lender receives the correct amount even if there are minor errors in the original contract.  For example, if the original payment were 0.05 too low, the contract finance charge would be lower than the correct amount for the stated interest rate.  However, a small difference such as this is not usually enough to warrant rejecting the contract because it won't put it out of Regulation Z tolerance.  By calculating the lender's retention first, the lender will receive the proper amount and the portion paid to the dealer will be slightly less because of the incorrect payment on the original contract.

The exactly-correct lender's retention is subtracted from the contract finance charge to determine the dealer reserve (assuming 100% is paid to the dealer).

In order to compensate the lender for early terminations, it is common to pay less than 100% of the dealer reserve to the dealer.  Thus the above dealer reserve is adjusted by the paid-to-dealer percentage (75% in this case) to determine the actual amount paid to the dealer.

The dealer advance is the sum of the note amount and the actual dealer reserve amount.

 

Hypothetical "buy" rate payment
(this payment can be calculated with any financial calculator, such as an HP 12C)
207.098557
Hypothetical "buy" total note 60 x 207.098557 = 12,425.91343
Hypothetical "buy" finance charge 12,425.91343 - 10,000.00 = 2,425.91343
Subtract above from contract 
finance charge to get the dealer reserve 
(assuming 100% is paid)
3,120.20 - 2,425.91343 = 694.28657
Multiply above by 75% to get
actual dealer reserve amount
694.28657 x 0.75 = 520.714928
Round result to nearest cent 520.71
Add note amount to paid dealer reserve to get the total advance to the dealer 10,000.00 + 520.71 = 10,520.71

Example #2 - With Odd Days

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This installment loan has a long first period.  The loan interest rate is 11.25%, and the bank "buy" rate is 8.90% with the bank paying 75% of the calculated dealer reserve.

The dealer reserve is calculated by the "Difference in Charges" method, which is the most common.  We have specified the Federal Calendar to measure the first period.  In this loan, the first period is 1 month + 13 days long.

 


Input dialog showing entered values


Output window showing results

Calculation methods
for Example #2

 

 

 

 

 

 

 

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There are several steps required to reach the final result of the dealer reserve and advance.  Note that in keeping with proper mathematical rules, no rounding is done on intermediate calculations: only the final result is rounded.

In the difference-in-charges method, a second, hypothetical loan is calculated using the lender's "buy" rate of 5.90%.  The finance charge on this hypothetical loan is the amount that the lender would retain if 100% of the dealer reserve were paid to the dealer (see below).

The calculated lender's retention is subtracted from the contract finance charge to determine the dealer reserve (assuming 100% is paid to the dealer).

In order to compensate the lender for early terminations, it is common to pay less than 100% of the dealer reserve to the dealer.  Thus the above dealer reserve is adjusted by the paid-to-dealer percentage (75% in this case) to determine the actual amount paid to the dealer.

The dealer advance is the sum of the note amount and the actual dealer reserve amount.

 

Hypothetical "buy" rate payment
(See calculating the payment 
with odd-days below)
232.967475
Hypothetical "buy" total note 60 x 232.967475 = 13,978.04850
Hypothetical "buy" finance charge 13,978.04850 - 12,053.85 = 1,924.19850
Subtract above from contract 
finance charge to get the dealer reserve 
(assuming 100% is paid)
2,975.55 - 1,924.19850 = 1,051.35150
Multiply above by 75% to get
actual dealer reserve amount
1,051.35150 x 0.75 = 788.513625
Round result to nearest cent 788.51
Add note amount to paid dealer reserve to get the total advance to the dealer 12,053.85 + 788.51 = 12,842.36
 

Calculating the payment 
with odd-days

None of the readily-available financial calculators such as the HP-12C can calculate a payment properly for a loan with a long first period.

On the right, we show the method to calculate 43 days of simple interest in the first period, and then 30 days (based on a 360-day year) for the remaining periods.

These formulas assume there is no negative amortization of the loan.  (There is no negative amortization in this example.)  The purpose of this example is to show the dealer reserve calculation therefore we have used the simplest calendar system to avoid complicating the calculation method.

See calendar systems and U.S. Rule for details on other methods.   

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Let  i = 5.90 / 1200.0
  Days = 43
     n = 60
  Note = 12053.85
    An = (1 - 1 / ((1 + i) ^ n) / i
   Add = An * (1 + i)

Then,
Pmt = Note x (1 + Days / 30 * i) / Add
    = 12053.85 x 1.00704722 / 52.10511107
    = 232.967475

WARNING:  This formula is only valid for loans with long-first periods that do not negatively amortize.  See U.S. Rule for details on negative amortization.

The payment calculation by the U.S. Rule is far more complicated but is required by most states.   PROM's programs such as the LoanMaker 523A PC and LoanMaker 623A Handheld products use the U.S. Rule in payment calculations.

To properly amortize this loan, one would take 43 days of interest when the first payment is made, and then 30 days (1/12th of a year) for each remaining payment.

Updated 18 Nov 2002

Amortization Schedule for Example # 2 Hypothetical Payment

Pmt   BOP Bal  Days     Int      Prin    EOP Bal
=== =========  ====  ======  ========  =========
 1  12053.850   43   84.946  -148.021  11905.829
 2  11905.829   30   58.537  -174.430  11731.398
 3  11731.398   30   57.679  -175.288  11556.110
 4  11556.110   30   56.818  -176.150  11379.960
 5  11379.960   30   55.951  -177.016  11202.944
 6  11202.944   30   55.081  -177.886  11025.058
 7  11025.058   30   54.207  -178.761  10846.297
 8  10846.297   30   53.328  -179.640  10666.657
 9  10666.657   30   52.444  -180.523  10486.134
10  10486.134   30   51.557  -181.411  10304.723
11  10304.723   30   50.665  -182.303  10122.421
12  10122.421   30   49.769  -183.199   9939.222
13   9939.222   30   48.868  -184.100   9755.122
14   9755.122   30   47.963  -185.005   9570.117
15   9570.117   30   47.053  -185.914   9384.203
16   9384.203   30   46.139  -186.828   9197.375
17   9197.375   30   45.220  -187.747   9009.627
18   9009.627   30   44.297  -188.670   8820.957
19   8820.957   30   43.370  -189.598   8631.360
20   8631.360   30   42.438  -190.530   8440.830
21   8440.830   30   41.501  -191.467   8249.363
22   8249.363   30   40.559  -192.408   8056.955
23   8056.955   30   39.613  -193.354   7863.601
24   7863.601   30   38.663  -194.305   7669.296
25   7669.296   30   37.707  -195.260   7474.036
26   7474.036   30   36.747  -196.220   7277.816
27   7277.816   30   35.783  -197.185   7080.631
28   7080.631   30   34.813  -198.154   6882.476
29   6882.476   30   33.839  -199.129   6683.348
30   6683.348   30   32.860  -200.108   6483.240
31   6483.240   30   31.876  -201.092   6282.149
32   6282.149   30   30.887  -202.080   6080.068
33   6080.068   30   29.894  -203.074   5876.994
34   5876.994   30   28.895  -204.072   5672.922
35   5672.922   30   27.892  -205.076   5467.847
36   5467.847   30   26.884  -206.084   5261.763
37   5261.763   30   25.870  -207.097   5054.666
38   5054.666   30   24.852  -208.115   4846.550
39   4846.550   30   23.829  -209.139   4637.412
40   4637.412   30   22.801  -210.167   4427.245
41   4427.245   30   21.767  -211.200   4216.045
42   4216.045   30   20.729  -212.239   4003.806
43   4003.806   30   19.685  -213.282   3790.524
44   3790.524   30   18.637  -214.331   3576.193
45   3576.193   30   17.583  -215.385   3360.809
46   3360.809   30   16.524  -216.443   3144.365
47   3144.365   30   15.460  -217.508   2926.857
48   2926.857   30   14.390  -218.577   2708.280
49   2708.280   30   13.316  -219.652   2488.629
50   2488.629   30   12.236  -220.732   2267.897
51   2267.897   30   11.150  -221.817   2046.080
52   2046.080   30   10.060  -222.908   1823.172
53   1823.172   30    8.964  -224.004   1599.169
54   1599.169   30    7.863  -225.105   1374.064
55   1374.064   30    6.756  -226.212   1147.852
56   1147.852   30    5.644  -227.324    920.528
57    920.528   30    4.526  -228.442    692.087
58    692.087   30    3.403  -229.565    462.522
59    462.522   30    2.274  -230.693    231.829
60    231.829   30    1.140  -231.828      0.001

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