Methodology.
Every formula, every source.

Fixed-rate amortization

The closed-form monthly payment for a fully amortizing fixed-rate loan with principal P, monthly rate r (annual ÷ 12), and N months:

Schedules are generated by tracking running balance: each month's interest is balance × r; principal is M − interest; balance becomes balance − principal. Floating-point rounding is corrected at the final payment so the schedule closes to zero.

Source: Standard time-value-of-money identity; equivalent to the present-value-of-annuity formula. Cross-checked against the example in CFPB Regulation Z, Appendix J.

Effective APR with origination fees

When a loan has an origination fee deducted from proceeds, the quoted rate is not the rate the borrower actually pays. The effective APR is the monthly rate r* that solves:

where P_net = P × (1 − fee%) and M is the payment computed on the gross principal. We solve for r* using Newton-Raphson with the analytic derivative, seeded at the quoted rate. Annualized APR is r* × 12.

Source: CFPB Regulation Z, Appendix J (Annual Percentage Rate Computations) — definition of APR as the rate that equates net proceeds to the present value of payments.

Mortgage: PITI + PMI + HOA

The displayed monthly payment is the sum of:

PMI applies when LTV exceeds 80% at origination. We model conventional PMI as an annual premium between 0.3% and 1.5% of loan balance (rate selected by LTV band), divided by 12. The calculator displays the month PMI drops off: the first month in which the scheduled balance reaches 78% of original purchase price, per HPA 1998.

Source: Homeowners Protection Act of 1998 (12 U.S.C. §4901 et seq.) for automatic PMI termination at 78% LTV. Conventional PMI rate bands from the major mortgage insurers' published rate cards (MGIC, Genworth, Radian). Benchmark mortgage rate from the Freddie Mac Primary Mortgage Market Survey.

Auto loan

Auto financing uses standard amortization on the financed amount, where:

Sales tax is computed on the post-trade-in price in states with a trade-in tax credit (most), and on the gross price in states without. The "upside-down" warning fires when the principal balance at any scheduled month exceeds the depreciated vehicle value, using a standard 15%-first-year / 10%-per-year depreciation curve.

Source: State-level trade-in tax treatment per the National Automobile Dealers Association (NADA) trade-in tax credit map. Depreciation curve approximates Edmunds True Cost to Own averages.

SBA 7(a) and 504

The SBA guarantee fee for 7(a) is tiered by loan size and maturity. For loans > 12 months:

The 504 program splits financing 50% conventional / 40% CDC debenture / 10% borrower equity (for most projects). The 504 calculator computes a blended effective rate from those tranches and the CDC processing fee (0.5% of debenture).

Source: SBA SOP 50 10 (current version), Chapter on Fees; SBA 504 Loan Program documentation for tranche structure.

Equipment financing & Section 179

Loan-vs-lease comparison computes the present value of after-tax cash outflows over the equipment's useful life, using the borrower's tax rate. Section 179 first-year deduction is capped at the current statutory limit ($1,160,000 for tax year 2023, indexed annually). Bonus depreciation phases down 20 points per year (80% in 2023, 60% in 2024, 40% in 2025, 20% in 2026, 0% in 2027) on qualifying property.

Lease residual handling: FMV leases assume return-at-term; $1-buyout leases are modeled as a capital lease and amortized like a loan.

Source: IRS Publication 946 (How to Depreciate Property), 26 U.S.C. §179, Tax Cuts and Jobs Act §13201 (bonus depreciation phase-down schedule).

Commercial real estate (balloon + DSCR)

CRE loans typically amortize over 20–25 years but balloon at 5, 7, or 10. Payment is computed on the amortization term; remaining balance at the balloon month is displayed as the refinance obligation. DSCR is:

where NOI = gross rent × (1 − vacancy %) − operating expenses. Cash-on-cash return is annual pre-tax cash flow divided by total cash invested (down payment + closing costs + reserves).

Source: Standard CRE textbook construction (e.g., Brueggeman & Fisher, Real Estate Finance and Investments); same definitions used in lender-prepared offering memoranda.

Invoice factoring & merchant cash advance

A factor rate of 1.30 on a 6-month advance is not a 30% rate — it's the multiple of principal repaid. The effective APR is the rate r* that solves:

For a 1.30 factor over 180 days with daily debit, this typically yields an APR in the 60–90% range. Solved with bisection seeded at 50%.

Source: Definitional — the APR is the rate that equates principal to the present value of repayments. See also CFPB Reg Z Appendix J; methodology echoed in Federal Reserve Bank of New York research on small-business financing transparency.

Student-loan income-driven repayment

For SAVE, PAYE, and IBR, the monthly payment is:

The discretionary income floor is a multiple of the federal poverty guideline for household size and state (225% for SAVE, 150% for PAYE/IBR). The applicable percentage of discretionary income is 10% for PAYE and IBR (new borrowers), 5% on undergraduate balances under SAVE, 10% on graduate balances under SAVE.

Forgiveness clocks: 20 years for SAVE undergraduate, 25 years for SAVE graduate, 20 years for PAYE, 25 years for IBR (pre-2014 borrowers). PSLF runs in parallel at 120 qualifying payments.

Source: Federal Student Aid repayment plan documentation; current-year HHS poverty guidelines (Federal Register).

Credit-card payoff

Credit-card minimum payments follow the standard issuer formula:

Payoff timeline iterates monthly: interest accrues at APR/12 on the average daily balance (approximated as month-end balance); the user's chosen payment is applied to interest first, principal second. The "minimum-only" path frequently never amortizes meaningfully on high APRs — this is the lesson the calculator exists to demonstrate.

Source: 1%-of-balance minimum formula is the post-2005 CARD Act industry standard; documented in CFPB Consumer Credit Card Market Reports.

Debt avalanche vs. snowball

Both methods accept the same total monthly budget. Avalanche applies the surplus (budget − sum of minimums) to the debt with the highest APR; once retired, the surplus + that debt's minimum cascades to the next-highest-APR debt. Snowball uses the same cascade logic but ranks by smallest balance.

Avalanche minimizes total interest paid; snowball minimizes time to first payoff. The calculator displays both side-by-side because the optimal answer depends on whether the user values mathematical efficiency or behavioral momentum more.

Source: Standard personal-finance constructions; behavioral case for snowball documented in Gal & McShane (2012), Journal of Marketing Research, "Can Small Victories Help Win the War?"

Investment growth

Future value of recurring contributions, compounded monthly:

where r is the monthly return (annual ÷ 12) and N is months. For "cost of waiting" analysis, we run the same formula on the foregone down payment for the buy-vs-wait comparison and present both outcomes net of inflation if requested.

Source: Standard time-value-of-money identity (future value of an annuity due / ordinary annuity).

Global cash flow

Global DSCR aggregates business CFADS with each 20%+ owner-guarantor's after-tax personal net cash flow, then divides by combined business and personal debt service:

Living expenses default to a household estimate scaled to household size and geography; the calculator allows overrides. Rental NOI from guarantor-owned properties rolls into personal income net of mortgage debt service. Distributions are added back when modeling the post-close structure (because the owner can choose to retain rather than distribute).

Source: SBA SOP 50 10 8 requirement to analyze the operating company AND each 20%+ owner-guarantor's repayment ability; FDIC Commercial Loans manual for the global cash flow construction used in examination.

Fixed charge coverage ratio

The EBITDAR-style FCCR test, as it appears in most middle-market credit agreements:

Rent appears on both sides because lease payments are a fixed charge alongside debt service, but EBITDA already deducts them — so we add them back in the numerator to compare apples to apples. A breach occurs when FCCR falls below the covenant floor (typically 1.10× or 1.20×); the calculator flags "watchlist" status when current FCCR is within 10% of breach.

Source: Standard middle-market credit-agreement covenant construction; example treatment in FDIC Commercial Loans and OCC Comptroller's Handbook.

Cash conversion cycle

The classic working-capital identity:

The line-of-credit sizing extension converts CCC into a working-capital gap and adds a seasonality multiplier and headroom buffer:

Default seasonality multiplier is 1.0 (smooth business); the calculator allows 1.2–1.5 for businesses with quarterly inventory builds.

Source: Standard corporate-finance textbook definitions (e.g., Ross, Westerfield, Jordan, Fundamentals of Corporate Finance). Banker's rule-of-thumb for LOC sizing from FDIC examination practice.

Bond yield, price, and spread

Plain-vanilla bullet bond pricing: the present value of coupons and face redemption at a single discount rate (the yield). For face F, annual coupon rate c, n periods at periodic yield r (annual yield ÷ frequency), per-period coupon C = F·c/freq:

Yield from price is solved by bisection over [−50%, 200%] (price is monotonically decreasing in yield, so bisection converges). Modified duration is computed from the closed-form Macaulay duration divided by (1 + r); convexity is the second-moment cash-flow weighting also closed-form. DV01 ≈ ModDur × Price × 0.0001. Spread to Treasury is the nominal yield difference vs. a user-supplied benchmark, expressed in basis points.

This calculator does not handle callable bonds (no yield-to-call), partial-period accrued interest, or full Z-spread / OAS computation. For non-callable Treasuries and most investment-grade corporates, the bullet model is accurate; for callables, see a Bloomberg YA terminal or open-source library like QuantLib.

Source: Fabozzi, Fixed Income Analysis (CFA Institute Investment Series); SIFMA standard bond conventions; U.S. Treasury Daily Yield Curve for benchmark yields.

Credit-risk approval heuristic

The "approval odds" widget on consumer-credit pages is a heuristic — not a lender decision. It scores a borrower on FICO band, DTI band, and LTV (where applicable), then maps to one of four bins: Strong / Likely / Borderline / Unlikely. The rate-range output is a band around the relevant Freddie Mac PMMS or industry average, widened by the borrower's score band.

The heuristic is calibrated to 2024–2026 industry-reported approval distributions; it does not pull credit, does not contact a lender, and does not generate a hard inquiry. It is intended to flag borderline applications before the user wastes a credit pull on one.

Source: Approval-band distributions calibrated against the Federal Reserve Survey of Consumer Finances and CFPB Consumer Credit Trends. Rate bands anchored to Freddie Mac PMMS (mortgage) and Federal Reserve G.19 Consumer Credit (auto, personal).