Lesson 3 of 25 · 6 min
How interest compounds on a carried balance
Unpaid card interest joins the principal, so a carried balance is a capitalizing loan on a monthly clock.
If the $79.94 from lesson 1 is not paid, it joins the principal. The next month's daily product runs on a larger figure. That is capitalization: unpaid interest becomes part of the balance that future interest is computed on. Track 1 lesson 14 named the move. This lesson puts twelve of those moves on a card.
Two clocks sit on the same $4,280 at 21.99 percent. Interest-only carrying, with the interest paid each month so the principal does not grow, costs $4,280 × 21.99 percent = $941.17 a year. The balance is still $4,280 at month 12. If the interest is not paid and is capitalized each month, the year is $4,280 × (1 + 0.2199/12)^12 = $5,322.07. Growth is $1,042.07. The extra $100.90 is interest charged on interest that was added along the way.
Track 5 lesson 12 separates a rate from a capacity: a rate is a cost in time, a capacity is a claim against an asset. A carried card is a capitalizing loan whose rate is doing that time-work on an unsecured balance. The posted 21.99 percent did not change between the $941.17 path and the $1,042.07 path. What changed is whether each month's $79.94-class charge stayed outside the principal or joined it.
Paying the month's interest holds the principal still. Leaving the interest unpaid raises the principal. The APR on the page is the same in both pictures.
Key terms
- Capitalization
- Adding unpaid interest to principal so the next period's interest is computed on a larger balance.
- Interest-only carrying
- Paying each month's interest and leaving the principal unchanged. The year is rate times starting balance.
- Compounded carrying
- Leaving the interest unpaid so it joins the principal. The year is starting balance times (1 + monthly rate)^12.
Worked example
One APR, two year-end balances
Wick & Pell Cards. Starting balance $4,280. Illustrative 21.99 percent APR. Twelve months.
- Interest-only year
- $941.17
- Monthly rate
- 0.018325
- Capitalized year-end balance
- $5,322.07
- Capitalized growth
- $1,042.07
- Gap between the two years
- $100.90
$4,280 × 21.99%. Balance still $4,280.
0.2199 ÷ 12.
$4,280 × (1 + 0.2199/12)^12.
$5,322.07 − $4,280.
Interest charged on capitalized interest.
The same 21.99 percent produced $941.17 with the principal held still and $1,042.07 with the interest left on the balance.
Check yourself
A Tallow Yard card starts at $3,600 at an illustrative 24.99 percent APR. What is twelve months of interest-only carrying, and what is the year-end balance if unpaid interest is capitalized each month?
A carried card balance is a capitalizing loan, the everyday version of interest added to a securities-backed balance in Track 5 lesson 12. Open A rate change is not a capacity change →
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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.