
Installment loans with long first
periods can easily result in the loan negatively amortizing
because the amount of interest due at the end of the first
period exceeds the monthly payment. The longer the loan
and higher the interest rate, the sooner it happens.
Most states have rules against
charging interestoninterest, which is what happens when a
loan negatively amortizes.
Table 1
below shows the maximum number of days in the first period
without negative amortization.
For lenders that offer up to 6
months to the first payment, there are very few
combinations that are safe to use without the U.S. Escrow
Rule method of calculation.

Rate

Term (in months)

12

24

36

60

84

120

180

240

5.00%

616

315

215

135

101

76

56

47

8.00%

391

203

141

91

70

54

43

37

10.00%

316

166

116

76

59

47

38

34

12.00%

266

141

99

66

52

43

36

33

15.00%

216

116

83

57

46

38

33

31

18.00%

183

99

72

50

42

36

32

30

20.00%

166

91

66

47

39

34

31

30

22.00%

153

84

62

45

38

33

31

30

25.00%

136

76

57

42

36

32

30

30

28.00%

124

70

53

40

35

32

30

30

30.00%

116

67

50

38

34

31

30

30

Table 1: Maximum number of days in
the first period of a monthly loan without negative amortization
Color Code: Max 45
days, 60 days,
90 days, 180 days, over 180 days.
Sample Loan
Illustrating the
U. S. Escrow Rule
Amortization Tables
Actual/365 (US Rule)
ActualtoFirst (US Rule)
Fed (360) Calendar (US Rule)
Fed (360) Calendar
(Actuarial)

The following sample loan was
selected to illustrate the differences between the various
calendar systems and the U.S.
Escrow Rule versus actuarial interest compounding.
By selecting a loan with a very
long first period (1 year) and a very high interest rate
(48%), the results from one calendar system to the next are
significant and easy to recognize. The high rate
assures that the loan would negatively amortize if the U.S.
Rule were not used.
In typical consumer loans,
negative amortization can occur even with just 31 days to
the first payment. See Table
1.
Using the U.S. Rule, this
unpaid interest is held aside in a separate escrow account
and no interest is charged on it. (This is how the
vast majority of consumer loan processing systems
work.)
In the last (Actuarial)
example, the interest is compounded monthly during the
first period of one year, and then the unpaid portion of it
is added to the principal balance, further increasing the
interest payments over the course of the loan.
We've selected a 6month loan
so we can show the amortization of the loan on a
monthbymonth basis for each of the four different
calendar systems in a compact
space.


Principal

500,000.00

Term

6 monthly payments

Interest
Rate

48.00%

Loan Date

May 9, 2002

First Pmt
Date

May 9, 2003

Last Pmt
Date

Oct 9, 2003


Actual/365 Calendar & US Rule Interest Accrual
Payment is $135,083.09
Payment

Date

Balance

Interest

Period

Escrow

Prin

Balance

0

5/9/02






500,000.00

1

5/9/03

500,000.00

240,000.00

365 days

104,916.91

.00

500,000.00

2

6/9/03

500,000.00

20,383.56

31 days


9,782.62

490,217.38

3

7/9/03

490,217.38

19,340.08

30 days


115,743.01

374,474.37

4

8/9/03

374,474,37

15,266.24

31 days


119,816.85

254,657.53

5

9/9/03

254,657.53

10,381.65

31 days


124,701.44

129,956.09

6

10/9/03

129,956.09

5,126.99

30 days


129,956.10

0.00

ActualtoFirst Payment
Calendar & US Rule Interest
Accrual Payment is $134,993.63
Payment

Date

Balance

Interest

Period

Escrow

Prin

Balance

0

5/9/02






500,000.00

1

5/9/03

500,000.00

240,000.00

365 days

105,006.37

.00

500,000.00

2

6/9/03

500,000.00

20,000.00

1 m


9,987.26

490,012.74

3

7/9/03

490,012.74

19,600.51

1 m


115,393.12

374,619.62

4

8/9/03

374,619.62

14,984.78

1 m


120,008.85

254,610.77

5

9/9/03

254,610.77

10,184.43

1 m


124,809.20

129,801.58

6

10/9/03

129,801.58

5,192.05

1 m


129,801.58

0.00

Federal Calendar & US Rule
Interest Accrual Payment is $134,993.63
Payment

Date

Balance

Interest

Period

Escrow

Prin

Balance

0

5/9/02






500,000.00

1

5/9/03

500,000.00

240,000.00

12 m

105,006.37

.00

500,000.00

2

6/9/03

500,000.00

20,000.00

1 m


9,987.26

490,012.74

3

7/9/03

490,012.74

19,600.51

1 m


115,393.12

374,619.62

4

8/9/03

374,619.62

14,984.78

1 m


120,008.85

254,610.77

5

9/9/03

254,610.77

10,184.43

1 m


124,809.20

129,801.58

6

10/9/03

129,801.58

5,192.05

1 m


129,801.58

0.00

Federal Calendar & Actuarial
Interest Accrual Payment is $146,834.59
Payment

Date

Balance

Interest

Period


Prin

Balance

0

5/9/02






500,000.00

1

5/9/03

500,000.00

300,516.11

12 m


153,681.52

653,681.52

2

6/9/03

653,681.52

26,147.26

1 m


(120,687.33)

532,994.19

3

7/9/03

532,994.19

21,319.77

1 m


(125,514.82)

407,479.37

4

8/9/03

407,479.37

16,299.17

1 m


(130,535.42)

276,943.95

5

9/9/03

276,943.95

11,077.76

1 m


(135,756.83)

141,187.12

6

10/9/03

141,187.12

5,647.47

1 m


(141,187.12)

0.00

The interest is compounded
monthly in the first period and is therefore significantly
higher than the US Rule example above. Also notice
how the loan negatively amortizes. This results in
higher interest charges for all of the remaining periods in
the loan. Even the last monthly interest charge is
higher by $455.42 ($5,647.47  $5,192.05) because of the
initial negative amortization. The total finance
charge on this loan is $71,045.76 higher than the previous
US Rule example  all because of interest compounding and
negative amortization.
The formula used to compute
this payment is:
Let i = 48.00 /
1200.0
Odddays = 330
n =
6
Note = 500000.00
An = (1  1 /
((1 + i) ^ n) / i
Then,
Pmt = Note x (1 + i) ^ (Odddays / 30) / An
= 500000.00 x 1.53945406 /
5.24213680
= 146834.5939
This method should
not be used for consumer loans, and is displayed
here for comparison purposes only. Note that many
payment formulas distributed by credit insurance
companies and others will compute the payment with the
illustrated compounding of interest and negative
amortization. This results in the charging of
interest on interest which is not permitted in most
states.
A variation of this formula
used by some insurance companies eliminates the
compounding during the oddday period, but does nothing
to prevent negative amortization:
Pmt = Note x (1 + Odddays / 30 * i) / An
= 500000.00 x 1.440000 /
5.24213680
= 137348.5713
which generates a somewhat
more reasonable payment, but one that is still $2,354.94
TOO HIGH compared with the U.S. Rule payment of
$134,996.63. This would still result in an
interest overcharge of $14,129.65.

