The Math behind the Fee Calculator

Overview

Here is how the Fee Calculator works:

7 parameters define the behavior of the cardholder per unit of time, and can be chosen by entering a value or from a pull-down menu:

  1. amount of $ direct-deposited,
  2. number of cash deposits made,
  3. number of cash withdrawals made,
  4. number of bills paid (or checks written),
  5. number of PIN-based purchase transactions (most cards don't charge for this, but there are a few unfortunate exceptions),
  6. number of overdrafts, (most cards don't charge for this, but many checking accounts do),
  7. number of calls to customer support.

The account (prepaid card or checking account) for which the cost calculation is made is defined by 15 parameters, including the discounted variations of such parameters and the threshold of such discounts, if applicable. When products do not change certain fees, then the value for such fees is simply set at zero.

  1. Non-discounted monthly maintenance fee
  2. Discounted monthly maintenance fee
    Note: a card could also have more than one level of discount, hence several thresholds, for example, a card may have a "discounted" fee above some level of usage and a "super discounted" fee above a further level
  3. Load/usage threshold above which the discounted maintenance fee applies
  4. Non-discounted ATM cash withdrawal fee
  5. Discounted ATM cash withdrawal fee
  6. Number of ATM cash withdrawals below which the fee is discounted
  7. Discounted bill-pay fee
  8. Non-discounted bill-pay fee
  9. Number of bills below which the bill pay fee is discounted
  10. Cash load fee
  11. Non-sufficient funds (attempt to overdraft) fee
  12. Non-discounted call fee to customer support center
  13. Discounted call fee to customer support center
  14. Number of calls below which the call fee is discounted
  15. PIN-based purchase transaction fee

The calculator makes a handful of justified simplifications:

  • There is no activation or purchase fee included in the evaluation, because cards sold at retail can (and do) charge such fees, but the same products opened online usually don't (because they have no easy means of charging them). These differences, which apply only to the first year of usage, do not reflect an inherent usage cost of the product;
  • If a card has both a non-discounted and a discounted monthly fee, it is assumed that the card-holder has a uniform behavior during the year, and receives either the non-discounted or discounted fee every month;
  • There are no cost parameters defined for direct deposit of funds in the card, nor for online access to the card account, since virtually all products in the market offer these for free;
  • Fees that may be charged for balance verification at the Point of Sale or at the ATM are also ignored since there is a free alternative online for all products (see above);
  • Currency exchange fees and foreign ATM access fees are ignored because most users never incur them.

The Fee Calculator produces Yearly Fees = F(User Behavior Parameters, Card Parameters) where F is an arithmetic function of all 7 user behavior parameters and all 15 product account parameters.

And now the math...

User behavior variables

Here are the 7 user behavior variables

  • DA= Amount of $ deposited per month
  • DC= number of cash deposits per year
  • WN= number of ATM cash withdrawals per month
  • CN= number of paper checks written per month
  • PTN = number of PIN-based purchase transactions per month
  • ON = number of accidental overdrafts per year
  • CCN = number of calls to a customer service agent per year

Account parameters

For each account of brand "X" the 15 parameters are:

  • XMF1 = Non-discounted Monthly Fee
  • XMF2 = Discounted Monthly Fee (e.g. = 0 if waived)
  • XMLT = Monthly Load Threshold above which the discounted monthly fee XMF2 applies
  • XAF1 = Non-discounted ATM Withdrawal Fee
  • XAF2 = Discounted ATM Withdrawal Fee (e.g. = 0 if free)
  • XMAT = Monthly ATM Withdrawals Threshold below which the discounted fee XAF2 applies (= 0 if no discounted/free ATM withdrawals)
  • XBP1 = Non-discounted Bill Pay Fee
  • XBP2 = Discounted Bill Pay Fee (e.g. = 0 if free)
  • XMBT = Monthly Bill Pay Threshold below which the discounted fee XBP2 applies (= 0 if no discounted/free bill payment)
  • XCLF = Cash Load Fee
  • XNSF = Non-Sufficient Funds Fee
  • XCCF1 = Non-discounted Call Center Fee
  • XCCF2 = Discounted Call Center Fee (e.g. = 0 if free)
  • XCCMT= Monthly Call Center Threshold below which the discounted fee XCCF2 applies (=0 if no discounted/free calls)
  • XPTF = PIN Transaction Fee

Note that a similar set of parameters can also specify the behavior of average bank checking accounts, with "X"="C".
The checking account parameters would be called CMF1, CMF2, ... CPTF where "C" stands for Checking.

Calculating the total yearly fees

The Yearly Fees are comprised of 4 families of fees:

  • YXMF = Yearly Monthly Fees for product X
    = IF(DA>XMLT, 12*XMF2, 12*XMF1)
  • YXBPF = Yearly Bill Pay Fees for product X
    = IF(BPN>=XMBT, (XMBT*XBP2+(BPN-XMBT)*XBP1)*12,BPN*XBP1*12)
  • YXAF = Yearly ATM Fees for product X
    = IF(WN>=XMAT, (XMAT*XAF2+(WN-XMAT)*XAF1)*12, WN*XAF1*12)
  • YXIF = Yearly Incidental Fees for product X
    = ON*XNSF + IF( CCN=XCCMT, (XCCMT*XCCF2+(CCN-XCCMT)*XCCF1)*12, CCN*XCCF1*12) + PTN*12*XPTF

YXF = Yearly Fees for product X= YXMF + YXBPF + YXAF + YXIF

The yearly cost of loading cash is calculated separately
YXDF = Yearly Cash Deposit Fees for product X= DC*XCLF
These fees are charged by the cash load network (e.g. GreenDot, MoneyGram, Western Union, ReadyLink, Repower ...) and not necessarily by the account issuer itself.