How the payoff is worked out
Each month, interest is added to the balance at one twelfth of the APR, then your payment is taken off. That repeats until the balance is gone; the last payment is usually smaller. For a target date, the payment is the standard loan payment for that balance, rate and number of months.
New balance = balance × (1 + APR ÷ 1200) − payment
Payment for a target = balance × r ÷ (1 − (1 + r)^−months), r = APR ÷ 1200 (or balance ÷ months at 0%). A payment must be more than balance × r, the first month’s interest, or the balance never falls.
Example: one debt
$5,000.00 at 18% APR with $200.00 a month.
- First month’s interest: $5,000.00 × 18% ÷ 12 = $75.00, so the first payment cuts the balance by $125.00
- After 31 full payments the rest is cleared by a last payment of $113.96: 32 months
- Total interest: $1,313.96; total paid $6,313.96
Example: a payment for a target date
The same $5,000.00 at 18%, paid off in 24 months.
- Payment: $249.62 a month
- Interest: $249.62 × 24 − $5,000.00 = $990.89
Example: three debts, avalanche and snowball
Card A $3,000.00 at 24% (minimum $90.00); Card B $5,000.00 at 18% (minimum $120.00); Loan $1,200.00 at 6% (minimum $60.00). Extra: $100.00 a month, so the monthly budget is $370.00.
- Avalanche (highest APR first: Card A 24%, Card B 18%, Loan 6%): debt-free in 32 months, interest $2,438.41
- Snowball (smallest balance first: Loan, Card A, Card B): debt-free in 32 months, interest $2,617.14
- Same finish month here; the avalanche costs $178.73 less in interest. Your own debts may differ.
Questions
What are the avalanche and snowball methods?
Both pay the minimum on every debt and send everything else to one target debt, then move on to the next once it is gone. The avalanche targets the highest APR first; the snowball targets the smallest balance first. Which one finishes with less interest depends on your numbers, and the calculator shows both for your debts.
Why does the extra amount stay the same when a debt is paid off?
The monthly budget is your minimums plus the extra, and it stays the same. When a debt is cleared its minimum is not spent elsewhere; it joins the target debt’s payment. That rolling forward is what speeds up the later debts.
What if my payment is too small?
If a single payment does not cover the first month’s interest, the balance would never fall, and the calculator says so and shows the interest. For several debts, it checks that your total budget covers the combined monthly interest.
How do I find the payment for a target date?
Choose the target mode and enter the months you want. The payment is the standard loan payment for that balance, rate and term.
How accurate is this for credit cards?
It adds one month of interest at the APR divided by 12 each month. Statements may work interest out differently, for example on a daily balance, and new purchases or fees are not included, so treat the result as an estimate.
Can I include a 0% debt?
Yes. Enter 0 for the APR. Under the avalanche it is paid last unless it has the smallest balance and you chose snowball.