Loan Payoff Calculator

Loan payoff math (explained)

A loan payoff calculator answers one question: “How long until my balance hits $0?” The catch is that interest is continuously added, and your payment has to cover that interest first, before any money reduces your principal (the amount you actually owe).

1) The core idea: each payment is split into interest + principal

For each payment period (monthly / bi‑weekly / weekly), the lender computes interest on your current balance:

Interest for one period = Balance × periodic_rate

Where the periodic rate is your APR divided by the number of payments per year. If APR is 7.5% and you pay monthly (12/yr), then:

periodic_rate = 0.075 / 12 = 0.00625 (about 0.625% per month)

Your payment then gets applied:

• Interest portion: the amount needed to cover the period’s interest
• Principal portion: whatever is left to reduce the balance

Principal paid = (Payment + Extra) − Interest

And the new balance becomes:

New balance = Old balance − Principal paid

2) The “minimum payment trap” (why payoff can fail)

If Payment + Extra is less than or equal to the interest that accrues each period, your principal paid becomes zero or negative — which means your balance will stay flat or even grow. That’s the classic trap with very small payments (common with revolving debt).

This calculator checks that condition. If your payment is too small, it warns you and shows the minimum payment needed to start reducing principal.

3) Why extra payments feel “magical” (they hit principal 100%)

A small extra payment often saves more than you expect because it reduces your balance earlier, which reduces future interest — a compounding effect in your favor. In this tool, the extra payment is assumed to be applied directly to principal each period.

4) What this calculator does internally

Rather than relying on a single closed‑form formula, we simulate your payoff schedule period by period (the same conceptual model lenders use in amortization tables):

1. Compute periodic interest from the current balance
2. Apply your payment (+ extra) and reduce the balance
3. Repeat until the balance reaches $0

This approach handles real‑world scenarios well: rounding, different payment frequencies, and extra payments.

5) Worked example

Suppose you owe $12,500 at 7.5% APR, paying $350/month, starting on January 1. Your first month’s interest is:

12,500 × (0.075/12) = 12,500 × 0.00625 = $78.13

Your principal paid in month 1 is:

350 − 78.13 = $271.87

New balance after the first payment:

12,500 − 271.87 = $12,228.13

Next month, interest is computed on the lower balance, so interest drops slightly and principal rises slightly. Over time, that acceleration is what finally kills the balance.

6) Extra payment comparison

Now add just $50 extra each month (so $400 total). That extra $50 reduces the balance faster, which reduces interest every month afterward. The results card shows:

• Time saved: how many months/years sooner you’re debt‑free
• Interest saved: the drop in total interest paid

Note: lenders may apply extra payments differently depending on loan type and rules. This is an estimate. Always verify with your lender for payoff quotes and exact dates.

How to use this calculator for better decisions

Use your current statement numbers

A payoff estimate is only as accurate as the inputs. Use your current balance and APR from your statement. If you recently made a payment, refresh your balance first.

Test “what if” scenarios

Try three runs: (1) current payment, (2) +$25 extra, (3) +$100 extra. Save each snapshot. You’ll quickly see the sweet spot where extra payments give the biggest payoff speedup for your budget.

Bi‑weekly payments can shorten payoff even without “extra”

Switching from monthly to bi‑weekly often results in one extra full payment per year (26 half‑months ≈ 13 monthly equivalents), which can shorten payoff. This tool will show the effect instantly.

Watch out for fees and prepayment rules

Some loans have prepayment penalties or require extra payments to be “principal only”. If the lender applies extra to future payments instead, the interest savings may be smaller.

Frequently Asked Questions

• Is the payoff date exact?

  It’s an estimate based on the numbers you enter and assumes on‑time payments with the chosen frequency. Real payoff dates can differ due to day‑count conventions, rounding, fees, escrow, or lender rules.

• What if my interest rate changes?

  This calculator assumes a fixed APR. If your rate changes (variable loan), rerun the calculator whenever the APR changes to update the payoff timeline.

• What does “total interest” include?

  It includes only the interest portion from each simulated payment. It does not include origination fees, late fees, insurance, taxes, or other charges.

• Why does bi‑weekly sometimes save a lot?

  Bi‑weekly schedules create more payment periods per year, and many borrowers effectively make the equivalent of one extra monthly payment annually. That accelerates principal reduction and reduces total interest.

• What if my payment is too low?

  If your payment does not cover interest, your balance won’t decrease. The calculator will show a warning and suggest the minimum payment needed to start reducing principal for your chosen frequency.

• Can I use this for credit cards?

  Yes for estimation, but credit cards can be trickier because rates change, minimum payments change, and fees may apply. For revolving balances, also try a dedicated Credit Card Payoff calculator.

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