## Saturday, August 6, 2022

### HP 12C: Cash Back vs Credit Card Interest

HP 12C: Cash Back vs Credit Card Interest

Introduction

If you have a credit card, chances are that you have a cash back program, where the company offers you cash back rate based on qualified purchases.  Is the benefit worth it?

HP 12C Program:  Cash Back vs. Interest

Store the following data:

PV:  current credit card balance

PMT:  qualified purchases

i% using [ g ] (12÷):  monthly credit card rate

R0 using [ STO ] 0:  cash back rate

This program assumes all purchases made qualify for the cash back rate.

Step #;  Step Key;  Key

01; 45, 14; RCL PMT

02; 45, 0;  RCL 0

03; 25; %

04; 31; R/S

05; 45, 13; RCL PV

06; 45, 14; RCL PMT

07; 40;  +

08; 45, 12; RCL i

09; 25; %

10; 31; R/S

11; 40; +

12; 43,33,00; GTO 00   (use GTO 000 on HP 12C Platinum)

Outputs:

1.  Cash back

2.  Interest charged on the balance and purchases

3.  New balance

Examples

Example 1:

Credit card balance:  \$1,000.00

Qualified purchases:  \$230.00

Credit card annual rate:  15%

Cash back rate:  5%

1000 [ PV ]

230 [ PMT ]

15 [ g ] (12÷)

5 [ STO ] 0

[ R/S ]:

11.50  [ R/S ]

15.38  [ R/S ]

1241.50

Cash back:  \$11.50

Interest:  \$15.38

New balance:  \$1,241.50

Example 2:

Credit card balance:  \$585.65

Qualified purchases:  \$176.19

Credit card annual rate:  16.79%

Cash back rate:  5%

585.65 [ PV ]

176.19 [ PMT ]

16.79 [ g ] (12÷)

5 [ STO ] 0

[ R/S ]:

8.81 [ R/S ]

10.66  [ R/S ]

772.50

Cash back:  \$8.81

Interest:  \$10.66

New balance:  \$772.50

Investigation:  Cash Back Benefit vs. Credit Card Interest

I then wondered, is there a point where the cash back gives a better benefit than the interest charged.

Consider the equation:

cash back benefits = monthly interest charge

purchases * cash_back% = (balance + purchases) * monthly_interest%

purchases * (cash_back% - monthly_interest%) = balance * monthly_interest%

purchases * (cash_back% ÷ monthly_interest% - 1) = balance

cash_back% ÷ monthly_interest% - 1 = balance ÷ purchases

Let the test ratio be defined as:

test ratio = cash_back% ÷ monthly_interest% - 1

Using the data from Example 2:

test ratio = 5 ÷ (16.79 ÷ 12) - 1 ≈ 5 ÷ 1.40 - 1 ≈ 3.57 - 1 = 2.57

For the cash back and interest to be equal, the purchases must equal balance÷2.57 or \$227.88.  Running the program, the cash back and interest charged is around \$11.38.

This means we will have to make a lot of qualified purchases.  Say if we spent \$400.00 in purchases, the cash back is \$20.00, with interest \$13.79, and the balance \$999.44.

To try to do this on a continuous basis poses several problems:  we still have to pay the balance otherwise we have to buy more each month to get the greater benefit.  Also, the lower the starting balance, the lower the minimum purchase requirement.

With a credit card rate of 16.79% (monthly about 1.40%) and cash back 5%, the test ratio is (5 ÷ 1.4 - 1) is 2.57.

A beginning balance of \$200.00 will require \$77.82 of qualified purchases (200 ÷ 2.57), while a beginning balance of \$500.00 will require \$194.55 in purchases.

Take care and have a great day,

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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