How this instrument works
This instrument answers a narrower question than deciding how to get out of debt in general: given exactly two balances and one fixed amount sent across both every month, how many months does the avalanche order — full budget at the higher-rate account first, minimum only on the other — actually take? A cardholder juggling a 22% card and a 12% personal loan is the typical user; a counselor sketching a payoff calendar for a client is another. The output is a month count, not a dollar total, because the number people plan a household around is when the last payment lands.
The math is the ordinary fixed-installment loan formula run backwards. Lenders use it to size a payment from a balance, a rate and a term; here it is solved for the term instead — the number of months a balance takes to reach zero under a fixed payment and compounding interest, using a natural-log identity rather than trial and error. Once the first account is cleared, a second formula compounds the untouched other balance forward by that same number of months before the same log solve runs again on the larger figure.
The sheet assumes both balances hold still — no new charges, no missed payments, no rate changes — and that the full combined budget lands every month without being redirected elsewhere. It only handles two balances; a household holding three or more needs the extras collapsed into one of the two slots or the calculation run in stages. It also stops short of the snowball order, smallest balance cleared first, which trades a longer timeline and more total interest for an earlier balance hitting zero — a real, non-arithmetic reason some people still prefer it.
- Enter Debt 1 balance (higher rate, paid first) and Debt 1 APR, % for the costlier account — the one that gets the full budget first.
- Enter Debt 2 balance (lower rate, paid second) and Debt 2 APR, % for the account that waits, accruing interest, until debt 1 is gone.
- Set Combined monthly payment budget, $ to the total sent across both accounts together each month.
- Read Months to clear debt 1 and Debt 2 balance once debt 1 is cleared, which already reflects the interest the second account accrued while ignored.
- Check Months to then clear debt 2 and Total months to be debt-free for the full payoff timeline.
Worked example — a $5,000 card ahead of a $3,000 loan
Set Debt 1 balance (higher rate, paid first) to $5,000 at Debt 1 APR, % = 22, Debt 2 balance (lower rate, paid second) to $3,000 at Debt 2 APR, % = 12, and Combined monthly payment budget, $ to 300 — every dollar goes at debt 1 first. Solving n1 = −ln(1 − r1·B1 ⁄ P) ⁄ ln(1 + r1) returns Months to clear debt 1 = 20.07: about a year and eight months of $300 payments against a balance where 22% interest consumes a large share of each early payment.
Across those same 20.07 months, the second account sat untouched and compounded: Debt 2 balance once debt 1 is cleared comes out to $3,663.17, up $663.17 from its starting $3,000 — the exact price of ignoring it in favor of the pricier one. With debt 1 gone, the full $300 turns to debt 2, and Months to then clear debt 2 works out to 13.09, giving Total months to be debt-free = 33.16 — a little over two years and nine months from the first payment to the last.
Questions
Why does the second balance grow before it shrinks?
Because it receives none of the combined budget while debt 1 is being cleared, yet interest keeps compounding on it every month regardless. In the $5,000-and-$3,000 example, the $3,000 second balance grows to $3,663.17 over the 20.07 months debt 1 takes — that growth is the calculated cost of directing every spare dollar at the higher-rate account first.
Why attack the higher-rate account first instead of splitting payments?
Interest is charged on whatever balance remains, so a dollar aimed at the highest rate stops the most future interest from accruing, which is why this order minimizes total interest paid across both accounts. Splitting the same budget evenly slows both payoffs and lets the higher-rate balance compound longer, typically costing more in total interest even though no balance grows meanwhile.
What happens if the combined budget can't cover debt 1's interest?
The month count never resolves. If Combined monthly payment budget, $ doesn't exceed debt 1's own monthly interest charge, the balance never shrinks and the logarithm inside n1 has no real solution, since compounding interest would outrun every payment. Raise the budget, or reduce the rate or balance it's fighting, before the timeline means anything.
How does this differ from the debt-snowball method?
Snowball orders payments by balance size, smallest first, for an earlier psychological win; this sheet fixes the order by rate — Debt 1 balance (higher rate, paid first) must hold the costlier account for the month counts to represent the avalanche method. Swapping which account goes in which slot computes a snowball-style timeline instead, and typically returns a longer Total months to be debt-free for the same two balances.
Does this calculation assume nothing else changes?
Yes. Both balances are treated as frozen except for the interest and payments this sheet applies: no new charges, no missed months, no promotional rate resets, and the full Combined monthly payment budget, $ landing every single month without exception. Real accounts drift from that in both directions, so treat the month counts as a clean baseline rather than a guaranteed calendar date.
Why use a logarithm instead of dividing the balance by the payment?
Dividing balance by payment only works when there is no interest; every real payment here splits between shrinking the balance and covering that month's interest charge, and the split changes every month as the balance falls. The logarithm is the closed-form solution to the same compounding equation lenders use to size a fixed payment, solved for the number of payments instead of the payment amount.
References
- CFPB — Debt collection and debt relief consumer tools
- Federal Reserve — Consumer Credit statistical release (G.19)
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.