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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
Reference URL's
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