CalcRay

Methodology

We show our work. Below are the core formulas and assumptions behind each calculator. All money math keeps full floating-point precision internally and rounds only for display.

These are standard, widely used finance formulas — there is nothing proprietary here. Each section states the equation, what every term means, and the assumptions behind it, so you can reproduce any result by hand or check it against another reputable calculator. The formulas below match the code in src/lib/finance.ts and are kept in sync with it.

Loan & mortgage amortization

Fixed-payment (amortizing) loans use the standard annuity payment formula:

Payment = P · r / (1 − (1 + r)−n)

where P is principal, r is the monthly rate (annual rate ÷ 12), and n is the number of payments. Schedules are simulated month by month so extra and one-time payments are handled exactly, with the final payment trimmed to land the balance on zero. The amortization schedule calculator's year-by-year table is a pure rollup of this monthly schedule into loan years — blocks of 12 payments from the first payment — not calendar years, so a partial final year is possible and year-1 interest will match a calendar-year tax form only for January starts.

Bi-weekly payments

Paying half the monthly amount every two weeks yields 26 half-payments — 13 full monthly payments per year. We model this as one extra (monthly ÷ 12) of principal each month, which is algebraically equivalent and avoids calendar drift.

Refinance break-even

Break-even months = closing costs ÷ monthly payment savings. Lifetime savings compares remaining interest on the current loan against total interest on the new loan, net of closing costs.

Mortgage discount points break-even

Both payments come from the annuity formula above, applied to the same principal and term — only the rate differs. Then: break-even months = points cost ÷ (base payment − bought-down payment), and net full-term savings = monthly savings × term − points cost. Break-even is computed in nominal dollars, with no discounting or opportunity-cost credit on the points cash, and no tax treatment of the points.

PMI removal (Homeowners Protection Act milestones)

We rebuild the scheduled amortization and report the first month the balance is at or below 80% and 78% of the home's original value — the Homeowners Protection Act thresholds for request-based cancellation and automatic termination on conventional loans. PMI paid to each milestone is months × monthly PMI. The model is schedule-only: no extra payments, no re-appraisal, and no midpoint backstop (PMI must also end at the loan's amortization midpoint, which binds only when high starting LTV meets a high rate). FHA mortgage insurance (MIP) follows different rules and is out of scope.

Debt snowball & avalanche

Both simulate month by month: interest accrues on each balance, minimums are paid, then all remaining budget targets one debt — the smallest balance (snowball) or the highest APR (avalanche). Freed-up minimums roll forward (the "snowball"). We always show the side-by-side interest and time difference.

Debt consolidation

The current path amortizes each debt independently at its entered payment, with no rollover between debts: months to debt-free is the slowest debt, and interest is summed across debts. A payment that does not cover a debt's monthly interest never pays off, and the tool says so. The consolidation path borrows total balances × (1 + fee% ÷ 100) — the origination fee is financed — with the payment from the annuity formula over the chosen term, and total cost = loan interest + fee.

FIRE number & Coast FIRE

The FIRE number is the portfolio that can sustain your spending indefinitely: FIRE number = annual spending ÷ withdrawal rate. At a 4% withdrawal rate this is equivalent to 25× annual spending (1 ÷ 0.04 = 25). The 4% figure comes from the safe-withdrawal-rate literature — William Bengen's 1994 analysis and the 1998 "Trinity study" (Cooley, Hubbard & Walz, Retirement Spending: Choosing a Sustainable Withdrawal Rate) — which found that a portfolio supporting an inflation-adjusted 4% first-year withdrawal historically survived a 30-year retirement with high probability. It is a historical heuristic, not a guarantee: it is based on past U.S. market data, assumes a stock-and-bond portfolio, and may understate the safe rate for very long retirements, which is why some planners prefer 3–3.5%. We let you set the withdrawal rate so you can apply your own assumption.

The Coast FIRE number is the present value of that target, discounted to today at your expected real return: Coast FIRE number = FIRE target ÷ (1 + real return)years to retirement. It is the amount that, invested today, grows to your target with no further contributions. Time to financial independence inverts the future-value-with-contributions annuity to solve for the number of years. Use real (inflation-adjusted) returns throughout so results are expressed in today's dollars.

Rent vs buy

We track the true economic cost of each path year by year. Buying's net cost subtracts home equity (appreciated value − selling costs − remaining loan). Renting's net cost subtracts investment gains on the cash a renter keeps liquid (the down payment and closing costs they didn't spend). Break-even is the first year buying's net cost falls below renting's.

Lease vs buy (car)

Total cost of ownership over your horizon. Leasing = down + payments + end fees. Buying = down + payments made + remaining balance − resale value. Both paths are credited the opportunity cost of their up-front cash at your chosen return.

Salary ↔ hourly

Effective hourly = annual pay ÷ hours actually worked, where worked weeks = working weeks − (PTO days ÷ 5). Because PTO is paid but not worked, it raises your real per-hour rate. All figures are gross (pre-tax).

Hourly to annual (with overtime)

Weekly = rate × hours + rate × OT multiplier × OT hours, then annual = weekly × paid weeks per year (52 minus unpaid weeks off). Base and overtime earnings are annualized separately to report overtime's share of gross income. Monthly is annual ÷ 12 by convention; bi-weekly is a true two-week paycheck (weekly × 2), which equals annual ÷ 26 only when all 52 weeks are paid. All figures are gross.

Pay raise

New pay = current × (1 + raise% ÷ 100) for percentage raises, or current + amount for dollar raises, with the equivalent percentage always reported back as (new − current) ÷ current × 100. Hourly pay is annualized first (rate × hours × weeks), and a per-hour raise is converted the same way. Cumulative extra income is deliberately linear — annual increase × years — with no compounding of future raises and no investment growth.

Assumptions & limits

References & primary sources

The concepts behind these calculators are documented by government and regulatory publishers. These are the primary sources we check our explanations against and link to from individual calculator pages:

Last reviewed: 2026-07-09