The formula, in one paragraph
Start with the balance, the APR and the monthly payment. Divide the APR by 12 to get the monthly rate, work out the exact months with a logarithm, round up to whole months, and the total paid is the full payments plus one final smaller payment. Six steps, all arithmetic.
Step 1: Find the monthly rate
The APR is an annual rate, but the payment is monthly, so divide by 12. At 19.99% a year, the monthly rate is 19.99% divided by 12, which is 1.6658% a month, or 0.0166583 as a decimal. The first month’s interest is the balance times this rate: $8,000 times 0.0166583, or $133.27. That number is a tripwire: if your payment is $133.27 or less, the balance never shrinks. A $350 payment clears it by $216.73 in the first month.
Step 2: Work out the exact months
The exact months come from the payoff formula: minus the natural logarithm of one minus the balance times the monthly rate divided by the payment, divided by the natural logarithm of one plus the monthly rate. At the example numbers that is minus the logarithm of 0.61924, divided by 0.0165211 — 0.47927 divided by 0.0165211, or 29.01 months.
Step 3: Round up to whole months
Payments come in whole months, so 29.01 months rounds up to 30 months — 2 years and 6 months. You cannot pay for 0.01 of a month, so the last month still needs a payment, even though it is a small one. Always round up, never down.
Step 4: Work out the final payment
The final payment is what is left after the full payments. After 29 payments of $350, the balance is $3.22; one more month of interest at 1.6658% makes the final payment $3.28. A tiny final payment is normal: it means the 29th full payment almost finished the job.
That box is the whole formula. The ceiling brackets mean round up to the next whole month; the logarithm unwinds the monthly compounding back into a count of months.
Step 5: Work out the total paid and the interest
The total paid is the full payments plus the final one: 29 times $350, which is $10,150.00, plus $3.28, which is $10,153.28. The interest is the total paid minus the balance: $10,153.28 minus $8,000, which is $2,153.28 — about 27% on top of the balance.
Step 6: Read the first payment
Every payment is the same $350, but what it is made of changes. The first month’s interest is $8,000 times 0.0166583, which is $133.27, so the principal in the first payment is $350 minus $133.27, which is $216.73. Early on, more than a third of each payment is interest; by the last payment, almost all of it is principal.
Worked example: $8,000 debt, 19.99% APR, $350 a month
Step 2: exact months = −ln(1 − $8,000 × 0.0166583 ÷ $350) ÷ ln(1.0166583) = 0.47927 ÷ 0.0165211 = 29.01 months.
Step 3: whole months = 30 months (2 yr 6 mo).
Step 4: final payment = $3.28 (balance $3.22 after 29 payments, plus one month of interest).
Step 5: total paid = 29 × $350.00 + $3.28 = $10,153.28. Interest = $10,153.28 − $8,000 = $2,153.28.
Step 6: first payment = $133.27 interest + $216.73 principal.
Answer: 30 months, $10,153.28 in all, $2,153.28 of interest.
What changes the payoff most
The payment moves the payoff fastest. At $250 a month the debt takes 47 months and costs $3,524.36 of interest; at $500 a month it takes 19 months and costs $1,381.87. A $5,000 debt at the same rate and payment takes only 17 months and $758.33 of interest — which is why the snowball attacks the smallest debt first. The rate moves the interest more than the months: at 12% the payoff takes 27 months and $1,128.36 of interest, while at 24.99% it takes 32 months and $2,975.11.
Order your debts smallest first
The snowball is the order, and the order is by balance. Take three debts — a $500 store card, a $2,000 credit card and an $8,000 loan — and the order is the $500 card first, then the $2,000 card, then the $8,000 loan. Pay the minimum on all three, throw every spare dollar at the $500 card until it is gone, then roll that whole payment onto the $2,000 card, then roll both payments onto the $8,000 loan. The avalanche method would order the same debts by APR instead, and it always pays less interest in total — but the snowball wins on motivation, because the first debt disappears fastest.
Work backwards from your deadline
When the deadline is fixed, run the formula in reverse. At 19.99%, $407.13 a month clears the $8,000 in 24 months, $741.04 a month clears it in 12 months, and $297.27 a month clears it in 36 months. And $350 a month clears at most $6,877.46 in 24 months — a bigger balance needs a bigger payment or more time.
Frequently asked questions
How do I calculate a debt snowball payoff by hand?
Divide the APR by 12 for the monthly rate, work out the exact months with the log formula, and round up to whole months. On $8,000 at 19.99% with $350 a month, the rate is 1.6658%, the exact months are 29.01, the payoff is 30 months.
How much interest will I pay on $8,000 at 19.99%?
$2,153.28 at $350 a month over 30 months. At $250 a month it is $3,524.36, and at $500 a month it is $1,381.87.
Why is my final payment so small?
Because the exact payoff is 29.01 months: 29 full payments of $350 leave only $3.22 of balance, and one month of interest makes the final payment $3.28.
What if my payment does not cover the interest?
Then the debt never shrinks. At the defaults the first month’s interest is $133.27, so a payment of $133.27 or less never pays the debt off.
How do I order my debts for the snowball?
Smallest balance first: a $500 store card, then a $2,000 credit card, then an $8,000 loan. Pay the minimum on all of them and roll each freed payment onto the next debt.
Try it: run your own numbers through the free debt snowball calculator — balance, APR and monthly payment, with the payoff time, total and interest broken out.