Downslope Finance

About the Math

On this page

  1. The amortization formula
  2. Month-by-month walkthrough
  3. Compounding conventions
  4. 0% / interest-free debt
  5. Excel validation (5 test cases)
  6. Avalanche vs. snowball

1. The amortization formula

In plain English: each month you're charged interest on what you still owe, and whatever's left of your payment chips away at the balance.

Every payment on an interest-bearing debt splits into two parts: interest owed on the current balance, and principal that actually reduces what you owe. Downslope calculates this month by month using the standard amortization recurrence:

interest = balance × monthly_rate
balance = balance + interest − payment

where monthly_rate = APR ÷ 12 (for monthly compounding)

This is equivalent to the closed-form used in Excel's NPER, IPMT, and PPMT functions. The loop terminates when balance ≤ $0.005 (half a cent) or after 1,200 months, a hard ceiling that catches degenerate inputs like a payment that barely covers interest.

Stuck debt detection. If a payment is at or below the monthly interest charge, the balance never decreases. Downslope flags this with a red warning rather than running an infinite loop. Fix: raise the payment or lower the APR.

2. Month-by-month walkthrough

Concrete example: $10,000 balance, 6% APR, $200/month payment.

Excel check: =NPER(6%/12, -200, 10000) → 57.68 (rounds up to 58 payments; final payment is smaller)

Month Opening balance Interest (0.5%) Principal Payment Closing balance
1$10,000.00$50.00$150.00$200.00$9,850.00
2$9,850.00$49.25$150.75$200.00$9,699.25
3$9,699.25$48.50$151.50$200.00$9,547.75
4–56…each month the interest charge falls as the balance shrinks…
57$335.67$1.68$198.32$200.00$137.35
58$137.35$0.69$137.35$138.04$0.00
Notice that as the balance falls, more of each payment goes to principal. This is why extra payments early in a loan save disproportionately more interest than the same dollar paid later.

3. Compounding conventions

Most loans charge interest once a month. Some credit cards charge it daily instead, which adds up to nearly the same total, but not exactly the same.

Most US loans compound monthly. Two common exceptions are handled by converting the stated APR to an equivalent monthly rate before running the loop:

Monthly (default for US mortgages, most loans)
monthly_rate = APR ÷ 12
Daily (many US credit cards)
monthly_rate = (1 + APR ÷ 365)365/12 − 1
Semiannual (Canadian mortgages)
monthly_rate = (1 + APR ÷ 2)2/12 − 1

Once converted, all three run through the same monthly loop. The difference between monthly and daily compounding at 20% APR is roughly $0.83 per $1,000 per year, small but measurable over a multi-year payoff.

4. 0% / interest-free debt

At 0% APR, there's no interest to subtract, every dollar you pay goes straight to the balance.

When a debt is marked 0% (no accruing interest), the monthly rate is set to exactly zero. The loop becomes simple division: balance ÷ monthly payment = months to payoff, with every dollar going directly to principal.

monthly_rate = 0
interest = balance × 0 = $0.00
balance = balance − payment
Promo APR expiration (Pro). Many 0% offers carry deferred interest: if the balance isn't cleared before the promo period ends, the lender back-charges interest on the original balance. Downslope lets you set an expiration date and shows a warning banner 90 days before, roughly the point at which you need to decide whether your current payment pace will clear the balance in time.

5. Excel validation (5 test cases)

These numbers aren't just asserted, you can check every one yourself in a spreadsheet.

Each row below can be independently verified in Excel or Google Sheets. The Months column matches =CEILING(NPER(rate, -pmt, balance), 1) and Total interest matches =pmt*months - balance adjusted for the smaller final payment.

Scenario Balance APR Payment/mo Months Total interest Excel formula
Personal loan (monthly) $10,000 6.00% $200 58 $1,538.04 =NPER(6%/12,‑200,10000)
Credit card (monthly) $5,000 19.99% $150 50 $2,357.17 =NPER(19.99%/12,‑150,5000)
0% promo card $2,400 0.00% $200 12 $0.00 balance ÷ payment = 12
Car loan (monthly) $25,000 5.50% $500 57 $3,445.78 =NPER(5.5%/12,‑500,25000)
High-rate card (near minimum) $8,000 24.00% $300 39 $3,686.52 =NPER(24%/12,‑300,8000)

To reproduce in Excel: enter balance in A1, APR in B1, payment in C1. Then =NPER(B1/12, -C1, A1) gives fractional months; =CEILING(NPER(B1/12,-C1,A1),1) gives the integer payoff month. Total interest: =CUMIPMT(B1/12, CEILING(NPER(B1/12,-C1,A1),1), A1, 1, CEILING(NPER(B1/12,-C1,A1),1), 0) (note: returns a negative number, negate it).

All five cases were computed from the same recurrence formula used inside Downslope. If you find a discrepancy of more than $0.01, please email dan@downslopefinance.com with your inputs.

6. Avalanche vs. snowball

Avalanche pays your most expensive debt first to save the most money overall. Snowball pays your smallest debt first for quick wins. Both get you to debt-free, just by different paths.

Both strategies pay minimums on all debts, then concentrate any extra budget on one target debt. The difference is which debt gets targeted.

When a debt is fully paid off, its freed minimum payment rolls into the budget for the next target. This is the "debt snowball" mechanic that Dave Ramsey popularised, and it applies to both strategies. The avalanche method just directs the growing budget at the highest-rate debt instead of the smallest balance.

Worked example

Two debts, $100/month extra available:

Avalanche, attack Debt A (20%) first

Payment to A$180/mo
A paid offmonth 20
B paid offmonth 22
Total interest$681.19

Snowball, attack Debt B ($1,500) first

Payment to B$160/mo
B paid offmonth 10
A paid offmonth 23
Total interest$840.08

In this example, avalanche finishes one month faster and saves $158.89 in interest. The gap widens when rate differences are larger (e.g., a 29.99% card vs. an 8% car loan). The gap narrows or reverses when balances are very close in size, because the snowball frees up the full minimum payment earlier.

Neither strategy is universally superior. The right choice depends on your specific balances, rates, and whether behavioural momentum matters for you personally. Downslope shows you both side by side so you can decide.

How Downslope simulates the portfolio

The portfolio simulator runs a month-by-month loop across all debts simultaneously. Each month it:

  1. Accrues interest on every active debt
  2. Pays the minimum on every active debt
  3. Sorts remaining active debts by the chosen strategy (rate or balance)
  4. Applies the extra budget to the top-ranked debt until it is paid off, then cascades to the next
  5. Rolls freed minimums into the budget for the following month
All calculations run entirely in your browser. No debt data is sent anywhere unless you use the AI game plan, which sends an anonymized summary to Anthropic. The formulas on this page match the behaviour of Excel's PMT, IPMT, PPMT, NPER, and CUMIPMT worksheet functions. This is a planning tool, not financial advice. Actual payoff timelines depend on your lender's billing cycle, minimum payment recalculation rules, and any fees not reflected here.