(11) When the iteration approach is used, it is expected that lators or computers will be programmed to carry all available decimals ughout the calculation and that enough iterations will be performed to virtually certain that the annual percentage rate obtained, when rounded decimals, is correct. Annual percentage rates in the examples below obtained by using a 10 digit programmable calculator and the iteration edure described above.

(c) Examples for the actuarial method. (1) Single advance transon, with or without an odd first period, and otherwise regular. The ral equation in paragraph (b)(8) of this section can be put in the owing special form for this type of transaction:

Example (1): Monthly payments (regular first period)

Example (ii): Monthly payments (long first period)

Amount advanced (A) = $6000. Payment (P)
Number of payments (n)
Unit-period

=

=

1 month. Unit-periods per year (w) = 12.
Advance, 2-10-78. First payment, 4-1-78.
From 3-1-78 through 4-1-78 = 1 unit-period.
From 2-10-78 through 3-1-78 = 19 days. (f
Annual percentage rate (I) = wi = .1182 = 11.82%

=

(t 1)
19/30)

Example (iii): Semimonthly payments (short first period)

Amount advanced (A) $5000. Payment (P)
Number of payments (n) 24.
Unit-period

1/2 month. Unit-periods per year (w)
Advance, 2-23-78. First payment, 3-1-78.
on 1st and 16th of each month.

Payments made

From 2-23-78 through 3-1-78 6 days. (t
Annual percentage rate (I) = wi= .1034 10.34 %

Example (iv): Quarterly payments (long first period)

Amount advanced (A) $10,000. Payment (P) $385.
Number of payments (n) = 40.'
Unit-period

(2) Single advance transaction, with an odd first payment, with
The general equation

or without an odd first period, and otherwise regular.
in paragraph (b)(8) of this section can be put in the following special
form for this type of transaction:

Example (1): Monthly payments (regular first period and irregular first payment)

Example (ii): Payments every 4 weeks (long first period and
irregular first payment)

=

Regular payment (P) - $38.31. Number of payments (n) = 12.
Unit-period = 4 weeks. Unit-periods per year (w) 52/4 = 13.
Advance, 3-18-78. First payment, 4-20-78.
From 3-23-78 through 4-20-78 = 1 unit-period.
From 3-18-78 through 3-23-78 = 5 days. (f 5/28)
Annual percentage rate (I) - wi-.2850

(t

1)

28.50%

(3) Single advance transaction, with an odd final payment, with or without an odd first period, and otherwise regular. The general equation in paragraph (b)(8) of this section can be put in the following special form for this type of transaction:

Example (1): Monthly payments (regular first period and irreg-
ular final payment)

Example (ii): Payments every 2 weeks (short first period and irregular final payment)

(4) Single advance transaction, with an odd first payment, odd al payment, with or without an odd first period, and otherwise regular. general equation in paragraph (b)(8) of this section can be put in the lowing special form for this type of transaction:

Example (1): Monthly payments (regular first period, irregular
first payment, and irregular final payment)

Advance, 1-10-78. First payment, 2-10-78.

From 1-10-78 through 2-10-78

1 unit-period. (t

Annual percentage rate (I) - wi.1090 = 10.90%

Example (11): Payments every two months (short first period, irregular first payment, and irregular final payment)

Number of payments (n) = 20. Unit-period- 2 months.
Unit-periods per year (w)

12/2 - 6.

Advance, 1-10-78. First payment, 3-1-78.

From 2-1-78 through 3-1-78 = 1 month.

through 2-1-78 = 22 days.

(t 0; f

From 1-10-78
52/60)

Annual percentage rate (I) - wi - .0730 7.30%

(2) Single advance transaction, with an odd first payment, with
The general equation

or without an odd first period, and otherwise regular.
in paragraph (b)(8) of this section can be put in the following special
form for this type of transaction:

Example (1): Monthly payments (regular first period and irregular first payment)

=

= 24.

Regular payment (P) $230. Number of payments (n)
Unit-period = 1 month. Unit-periods per year (w) = 12.
Advance, 1-10-78. First payment, 2-10-78.
From 1-10-78 through 2-10-78 = 1 unit-period. (t
Annual percentage rate (I) = wi= .1008 10.08%

1; f = 0)

Example (ii): Payments every 4 weeks (long first period and
irregular first payment)

=

Regular payment (P) $38.31. Number of payments (n) = 12.
Unit-period 4 weeks. Unit-periods per year (w) 52/4 - 13.
Advance, 3-18-78. First payment, 4-20-78.
From 3-23-78 through 4-20-78 - 1 unit-period. (t
From 3-18-78 through 3-23-78

5 days. (f

5/28) 28.50%

Annual percentage rate (I) = wi-.2850

1)

(3) Single advance transaction, with an odd final payment, with or without an odd first period, and otherwise regular. The general equation in paragraph (b)(8) of this section can be put in the following special form for this type of transaction:

Example (1): Monthly payments (regular first period and irreg-
ular final payment)

Unit-period = 1 month. Unit-periods per year (w) = 12.
Advance, 1-10-78. First payment, 2-10-78.

From 1-10-78 through 2-10-78 = 1 unit-period. (t
Annual percentage rate (I) = wi= .1050 10.50%

1; f = 0)

Example (11): Payments every 2 weeks (short first period and irregular final payment)

(4) Single advance transaction, with an odd first payment, odd al payment, with or without an odd first period, and otherwise regular. general equation in paragraph (b)(8) of this section can be put in the lowing special form for this type of transaction:

Example (1): Monthly payments (regular first period, irregular
first payment, and irregular final payment)

Number of payments (n) = 24.

Unit-periods per year (w) = 12.

Unit-period = 1 month.

Advance, 1-10-78. First payment, 2-10-78.

From 1-10-78 through 2-10-78 1 unit-period. (t 1; f = 0)
Annual percentage rate (I) - wi-.1090

10.90%

Example (11): Payments every two months (short first period, irregular first payment, and irregular final payment)