Lesson 5 of 25 · 6 min
Late fees as arithmetic
A late fee joins the balance, so the rate then accrues on a larger principal.
A late fee is a charge. If it is not paid as cash, it is added to the balance the rate already accrues on. Track 5 lesson 14 is a prior-period adjustment: a new amount posted for a period that looked settled. An unpaid late fee is that adjustment on a household product. The period of the miss is not reopened as a conversation. It is reopened as a larger principal.
Three invented fees. The car still prints $40. The card prints $41. The mortgage prints $88.93, which is 4.5 percent of an invented $1,975.20 of principal-and-interest, a share some contracts cap. The three figures are not interchangeable. Each is a charge on one product's missed cash. What they share is the next step: unpaid, they sit on the balance.
Three card fees across three months are 3 × $41 = $123. If those $123 are unpaid, they join the $4,280. The illustrative 21.99 percent now accrues on $4,403. A fee that looked like a one-line charge has become principal. That is the capitalization already taught on a card: a posted amount that is not collected as cash becomes a piece of the balance the daily rate multiplies.
The $40, the $41 and the $88.93 are charges. Unpaid, they are principal. The rate does not ask which line they came from.
Key terms
- Late fee
- A charge on a missed installment. Car $40, card $41, mortgage $88.93 in this invented book.
- Capitalized fee
- A fee that was not paid as cash and so joined the balance the rate accrues on.
- Prior-period adjustment, household form
- Track 5 lesson 14: a new amount for a period that looked settled. The unpaid fee is that amount.
Worked example
Three fees, one of them becoming principal
Illustrative figures scaled down so the arithmetic is followable; they are not the reported amounts. Car fee $40. Card fee $41. Mortgage fee $88.93 on $1,975.20 PI. Three unpaid card fees.
- Mortgage fee as a share of PI
- 4.5%
- Three card fees
- $123
- Card balance before the fees join
- $4,280
- Balance after unpaid fees capitalise
- $4,403
- What 21.99% now multiplies
- $4,403
$88.93 ÷ $1,975.20. Some contracts cap this.
3 × $41.
$4,280 + $123.
The fees are inside the principal.
Three $41 fees are $123. Unpaid, they make the $4,280 into $4,403, and the rate accrues on the new figure.
Check yourself
Three invented $41 card fees are unpaid on a $4,280 balance at 21.99 percent. What do the fees total, what is the new balance if they capitalise, and what is that the everyday version of?
A late fee is a charge added to the balance, the everyday version of Track 5 lesson 14's prior-period adjustment: a new amount for a period you thought was settled. Open What a prior-period adjustment is →
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.