01-07-2017, 05:38 PM

HP 12C: Rule of 78

When a mortgage, a loan, a lease, or other annuity is paid early, we can determine how much interest rebate is due by the Rule of 78:

Rebate = ( (n – k + 1) * FC ) / ( (n + 1) * n)

Where:

n = the length of the annuity (number of periods)

k = the period where the loan is paid off

FC = total interest, finance charge = PMT * n – PV

The program will require the user to input and compute the annuity variables [ n ], [ i ], [ PV ], and [PMT] ([FV] if a balloon payment is required). Then enter the period # where the loan is paid off (k), and press [R/S].

Program:

Keep in mind: this is done on the HP 12C (regular). For the HP 12C Platinum, the code for Last X is 43, 40 ([ g ] [ + ])

STEP; KEY; CODE NUMBER

01; STO 1; 44, 1

02; RCL PMT; 45, 14

03; RCL n; 45, 11

04; *; 20

05; RCL PV; 45, 13

06; +; 40

07; CHS; 16

08; STO 0; 44, 0

09; RCL n; 45, 11

10; RCL 1; 45, 1

11; -; 30

12; 1; 1

13; +; 40

14; *; 20

15; RCL 1; 45, 1

16; ÷; 10

17; LST x; 43, 36

18; 1; 1

19; +; 40

20; ÷; 10

21; GTO 00; 43, 33, 00

Example: On a 48 month purchase of a $20,000 car, financed at 5%, the purchaser pays the car off early after 24 payments (k = 24). What is the rebate?

Output:

Find the payment:

[ f ] [X<>Y] (CLEAR FIN) (if necessary)

48 [ n ]

5 [ g ] [ i ] (12÷)

20000 [ PV ]

[ PMT ] (payment = -460.59)

24 [R/S]

Rebate: $87.84

Source: Rosenstein, Morton. Computing With the Scientific Calculator Casio: Tokyo, Japan. 1986. ISBN-10: 1124161430

When a mortgage, a loan, a lease, or other annuity is paid early, we can determine how much interest rebate is due by the Rule of 78:

Rebate = ( (n – k + 1) * FC ) / ( (n + 1) * n)

Where:

n = the length of the annuity (number of periods)

k = the period where the loan is paid off

FC = total interest, finance charge = PMT * n – PV

The program will require the user to input and compute the annuity variables [ n ], [ i ], [ PV ], and [PMT] ([FV] if a balloon payment is required). Then enter the period # where the loan is paid off (k), and press [R/S].

Program:

Keep in mind: this is done on the HP 12C (regular). For the HP 12C Platinum, the code for Last X is 43, 40 ([ g ] [ + ])

STEP; KEY; CODE NUMBER

01; STO 1; 44, 1

02; RCL PMT; 45, 14

03; RCL n; 45, 11

04; *; 20

05; RCL PV; 45, 13

06; +; 40

07; CHS; 16

08; STO 0; 44, 0

09; RCL n; 45, 11

10; RCL 1; 45, 1

11; -; 30

12; 1; 1

13; +; 40

14; *; 20

15; RCL 1; 45, 1

16; ÷; 10

17; LST x; 43, 36

18; 1; 1

19; +; 40

20; ÷; 10

21; GTO 00; 43, 33, 00

Example: On a 48 month purchase of a $20,000 car, financed at 5%, the purchaser pays the car off early after 24 payments (k = 24). What is the rebate?

Output:

Find the payment:

[ f ] [X<>Y] (CLEAR FIN) (if necessary)

48 [ n ]

5 [ g ] [ i ] (12÷)

20000 [ PV ]

[ PMT ] (payment = -460.59)

24 [R/S]

Rebate: $87.84

Source: Rosenstein, Morton. Computing With the Scientific Calculator Casio: Tokyo, Japan. 1986. ISBN-10: 1124161430