Methodology

General principles

Three rules govern every calculation on this Site:

1. Browser-only math. The Tools run as pure-client computation. Your inputs never leave the device unless you put them into a shareable URL — and even then, they go only to the next human you send the URL to, not to a server. There is no telemetry on input values.
2. One formula, one tool. Each Tool answers one question and uses the same math your lender does, so the number you get from us should match the number your lender quotes (modulo whatever fees they add).
3. Transparent omissions. Real finance has taxes, fees, inflation, balloon payments, variable rates, and other complications. We ignore most of these. This page documents every simplification so you can decide whether they matter for your case.

Loan comparison

Each loan is treated as a fixed-rate, fully-amortizing installment loan — the same math your lender uses to generate the monthly payment quote:

PMT = P × i / (1 − (1 + i)⁻ⁿ)

where P is principal, i is the monthly rate (APR / 12), and n is the number of months. Ranked by total repaid (principal + interest). The cheapest loan is the one with the lowest sum of all monthly payments.

We also surface monthly payment and total interest as secondary columns so the ranking isn't a black box. When the inputs are realistic, the cheapest loan is usually the one with the lowest monthly payment — but shorter-term loans may have a higher monthly payment and a much lower total cost, which is the comparison the ranking is built to surface.

What this doesn't include: origination fees, prepayment penalties, variable rates, balloon payments, taxes on the interest deduction (mortgage interest can be deductible — that would shift the ranking for some borrowers), points paid at closing, and any lender-specific discounts (rate buy-downs, autopay discounts, relationship pricing). For an apples-to-apples comparison of pre-discount offers, the ranking is accurate; for a real-world apples-to-apples comparison, add those costs to each loan's principal before entering it.

Amortization with extra payments

Standard amortization with the extra payment applied to every monthly payment after month 0. We compute the baseline schedule (no extra) and the accelerated schedule (with extra) and report the difference in months and total interest.

The schedule is generated by walking the loan month by month with the actual remaining balance, not by a closed form that drifts at the last row. Each month:

1. Compute interest as balance × monthlyRate.
2. Apply the payment (regular + extra) — paying down principal.
3. If the new balance is less than the upcoming payment, mark the loan as paid off and exit early.
4. Otherwise record the row, increment the month, and continue.

This catches edge cases the closed form misses: the final payment is often a few cents off the regular payment, the loan pays off ahead of schedule when extra payments exceed the interest accrual, and small rounding differences don't compound into nonsense over a 30-year amortization.

What this doesn't include: time-value-of-money discounting of saved interest (every dollar you pay in month 12 is "cheaper" in present-value terms than the same dollar in month 36), and the time-of-tax impact of the mortgage interest deduction when refinancing or paying early materially shifts your average balance. For most consumer loans (4-7 years) the present-value effect is small enough to ignore.

Borrow vs invest

Two scenarios, compared at the moment the loan is paid off:

• Borrow scenario: keep the cash invested at the expected annual return, pay the loan back on schedule. Net position = investment growth − total loan payments.
• Pay-cash scenario: spend the cash now, take no loan, no future investment. Net position = $0 (you spent the cash).

The borrow scenario wins when the investment growth exceeds the total interest paid. The break-even point is exactly the loan APR — below that rate, borrowing loses; above it, borrowing wins. The Tool marks the winner with a green delta and the loser with a red delta, plus the absolute dollar gap at the end.

We deliberately compare at loan-payoff-date rather than at some arbitrary future date, because that's the moment the comparison has a clean answer. (Comparing "5 years from now" for a 30-year mortgage is comparing two unfinished movies.)

What this doesn't include:taxes on investment gains, taxes on mortgage interest deduction, the fact that "expected return" is a guess not a guarantee, inflation, and any liquidity / cash-flow flexibility value of holding cash. The methodology intentionally ignores these so the model stays legible — but a real financial decision should weigh them too. See a fiduciary advisor if the amounts are large enough to matter.

What all tools share

• No tax modeling. Every dollar is a pre-tax dollar. Real returns are post-tax. The tax drag on long-term capital gains in the US is roughly 15-20% federal for most taxpayers; layered onto a 7% expected return, the after-tax expected return is closer to 5.5-6%.
• No inflation modeling.Everything is in nominal dollars, not today's purchasing power. For long horizons (15+ years) this matters; for a 5-year auto loan, it doesn't.
• No "guaranteed" returns. The 7% expected return you typed is a guess, not a contract. Use a low number (3-5%) for a conservative estimate; use a higher one (8-10%) for an optimistic estimate; treat the difference between them as the real uncertainty.
• Browser-only calculations. Nothing is sent to a server. Refreshing clears state unless you save a scenario (localStorage) or use the shareable URL.
• Fixed-rate assumption. Adjustable-rate loans are treated as fixed at the input rate over the entire term. If your ARM has a 5/1 structure, this tool will understate the long-run cost of the loan.
• No judgment. The Tool shows you the math. It does not tell you to take the loan or skip it. The decision is yours.

When these simplifications matter

For a 5-year, $25,000 auto loan at 6% APR with no prepayment, the simplifications on this page move the final number by less than 1%. You don't need fancier math.

For a 30-year, $400,000 mortgage with a 30% marginal tax bracket, fee structure, points at closing, and a plan to hold the loan for the full term, you absolutely do. These Tools give you a directional read on the question in the first sentence of each section; for a real six-figure decision, confirm with a spreadsheet or a fiduciary who is paid by you and not by commission.

Credits

The math comes from standard installment-loan formulas (the PMT formula) and ordinary present-value arithmetic, as covered in any introductory finance textbook. The Site code is original. Implementation differences from textbook versions: month-by-month walk instead of closed form (for accuracy on the last row), explicit handling ofpaying-off-early (when extra payments exceed the interest accrual), and the explicit nominal-vs-real dollar distinction on this page.

If you find a discrepancy between a calqcomp output and your spreadsheet or your lender's schedule, that is a bug worth reporting.