credit card grace period

I just came across the topic of credit card grace period, and could not find a consistent answer on exactly how it is supposed to apply in more complex situations than a monthly full payment.

On the back of the bill, it is defined thusly

We accrue periodic finance charges on a transaction, fee, or finance charge from the date it is added to your daily balance until payment in full is received on your account. However, we do not charge periodic finance charges on new purchases billed during a billing cycle if we receive both payment of your New Balance on your current statement by the date and time your payment is due and also payment of your New Balance on your previous statement by the date and time your payment was due.

This still is fairly ambiguous. In order to find out how this works exactly, to the cent, I did a simple test and found out.

First, some observations and terms.

  • For the sake of argument, let us say the credit card has a grace period of “at least 20 days,” and the method of “computing the balance on purchases” is the “average daily balance method (including new purchases)” — the standard terms these days. Let’s say the the credit card billing cycle ends on the 8th of each month, and the due date is always the 28th. (The difference in the two dates is the “grace period.”) Let’s ignore misc. fees.
  • During any billing cycle, say, the n-th billing cycle lasting from 3/9 to 4/8, all the charges and whatnot are computed on the last day of the billing cycle, that is, the billing date.
  • To compute the bill, a daily running balance sheet is initialized with the ending balance of 3/8. Then, for each day, that day’s charges and credits are added and then a daily interest is calculated and potentially added. Any negative number is assumed to be $0 for interest calculations (no they don’t pay you back interest.) Purchases are added on the day they are made, not when the transactions post.
  • When we say the balance of a bill (from 1/9 to 2/8 for example) was paid in full on time, it means, the credits and payments applied up to 2/28 are no less than the ending balance on 1/8. This calculation isn’t concerned with “new purchases” and interest and charges after 2/8.

Okay, note that grace period and interest calculation determination is a two-state machine. Due to the dislocation of the due date from the billing date, it gets… complicated:

The best way to understand this is to imagine that when a bill is computed, in addition to the daily balance sheet given above (let’s call it A) which includes everything, there are two more run in parallel. There is one (call it B), which has the new purchases of the billed cycle withheld from consideration (and hence interest charges) and added back as the last calculation. There is another one (call it C), which has the new purchases of the billed cycle witheld from consideration and added back on the last day of the cycle, as well as has the purchases of the previous cycle withheld from consideration but added back on the due date of the previous cycle.

Which balance sheet ends up getting used is determined by which of the four states governs the current billing cycle. The state is determined by looking at whether the previous bill was paid in full and whether the bill before that was paid in full. To be concrete, say the current billing cycle (3rd) is from 3/9 to 4/8. The previous billing cycle (2nd) is from 2/9 to 3/8 with a due date on 3/28, and the previous one to that (1st) is from 1/9 to 2/8 with a due date on 2/28. This is summarized in the following table:

Balance sheet of 3rd billing cycle (* PIFOT = paid in full on time)

1st bill PIFOT 1st bill not PIFOT
2nd bill PIFOT C B
2nd bill not PIFOT A A

Initial conditions are PIFOT, PIFOT, so on opening the account, you start with balance sheet C on the first bill.

To analyze this further, there two steady conditions: always pay on time, and always have a balance. Those are easy cases, because either there is never any interest charged or there is always interest charged on everything. It gets interesting only when switching between the two steady conditions. Consider these:

1st bill PIFOT, 2nd bill not PIFOT: Let’s say the balance ending the bill (the “1st” bill) from 1/9 to 2/8 was paid in full on time on 2/28, but the balance ending the bill (the “2nd” bill) from 2/9 to 3/8 was not paid in full on time on 3/28. The effect shows on the bill (“3rd” bill) covering the dates 3/9 to 4/8. Since the 1st bill was paid on time, but the 2nd bill was not paid in full on time, unpaid purchases made from 2/9 to 3/8 essentially won’t be entirely interest free, because from 3/9 to 4/8, interest will be added daily starting from the closing balance of 3/8. Depending on prior states, the purchases could have still been interest free from when they were made up to 3/8. Furthermore, new purchases made from 3/9 to 4/8 would be added to the daily balance immediately and be charged interest from the day of purchase.

1st bill not PIFOT, 2nd bill PIFOT: Let’s say the ending balance of 1st bill (from 1/9 to 2/8) was not paid in full on time on 2/28, but the ending balance of the 2nd bill (from 2/9 to 3/8) was paid in full on time on 3/28. Again, the effect shows on the 3rd bill generated on 4/8. Let’s say the ending balance of the 2nd bill was paid in full even a little ahead of time, say on 3/26. However, this doesn’t mean the balance is $0 or less on 3/26 or afterwards, since there has been interest and new purchases since 3/8. So on the 3rd bill, there will be full daily interest from 3/9 to 4/8 on everything including residual balance, interest, as well as new purchases from 3/9 to 4/8.

There are several implications. Once on balance sheet A, it takes two periods to flush out the states to return to balance sheet C. But if prompt payment is made, it doesn’t take long to recover, since B and C have no monetary difference if there is no opening balance to a bill. Consider the following scenarios:

One scenario is, if all payments are made in full, and one payment is missed, then, what should happen is to immediately pay the balance in full and refrain from making purchases until the end of the billing cycle during which the missed due date falls. Example: if payment is missed on 1/28, make no purchases until 2/9. Interest will effectively accrue on the cycle’s starting balance from the beginning of the cycle until its payment (can be considered as applying to this balance first), and interest will also accrue on new purchases from the day of the purchase to the day of the payment. To make sure this balance returns to $0 immediately, you also have to pay all interest up to the day of payment as well, not just the net balance. This can easily be computed if you have all the information, but otherwise you’d have to err on the side of caution and make a bigger payment. If you just pay off the net balance, interest will continue to accrue on the interest forever (theoretically) into future billing cycles, because even if the bill tells you the amount on the billing date, by the time you pay it, more interest will have accrued. In reality, underflow stops this problem.

A second scenario is, if there is a 0% promotional APR, and it is in effect until some date that somehow doesn’t coincide with the usual due date of some particular cycle, then… if the end date falls within the first part of a cycle before the due date, then, just pay off the balance on that date; but if it falls within the second part of the cycle after a billing cycle due date, then the balance up to the prior statement must be paid in full on the due date of the cycle during which the promotion ends. Otherwise, much pain ensues.

So finally what is the “grace period”? It’s the number of days from the ending date of a bill that you have, to apply payments and credits to reduce its ending balance to $0, in order to keep the credit card loan interest-free, retroactive to the beginning of the grace period.

Comments

  1. jesse
    January 25th, 2008 | 14:43

    If you want to get zero finance charges on your purchases, make a small insignificant purchase on your card and send in a payment of $100 or more depending on your purchasing habits, the very next day. You will receive a credit on your account. It will stay there for 90 days if you don’t make a purchase before it is refunded as a check. All purchases made while there is a credit on your account are interest free. Keep a credit on your account and keep using the account interest free.

  2. me
    January 28th, 2008 | 2:33

    Yes, but that’s not really interest-free, because your $100 is also loaned to the credit card issuer interest-free. If you will keep the total balance below $0 at all times, then a debit card will do.

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