This page documents exactly how each calculator on TaxAndLoans arrives at its numbers: the formula it uses, where any underlying data comes from, and the known limitations you should keep in mind before relying on a result. If you want the short version, every calculator also has a “Show the math” section with your own numbers substituted into the formula.
Mortgage Calculator
Formula
Formula: the standard amortizing-loan payment formula, M = P × [r(1+r)n] / [(1+r)n − 1], where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments.
M = P × [r(1+r)n] / [(1+r)n − 1]
Data source
Data source: the core payment calculation needs no external data — it's purely formula-based on the loan amount, rate, and term you enter. The optional property tax field auto-fills with each state's average effective property tax rate from the Tax Foundation, which you can overwrite with your own figure at any time.
Known limitations
Limitations: ARM calculations use only the initial fixed-rate period and don't model how payments change after the rate starts adjusting. Property tax rates are state averages, not your home's actual assessed value, so your real bill may be higher or lower.
Worked example
Take a $350,000 loan at 6.5% for 30 years (360 monthly payments). The monthly rate is r = 0.065 ÷ 12 = 0.005417, and n = 360.
M = 350,000 × [0.005417 × (1.005417)360] / [(1.005417)360 − 1] = $2,212.24/month
Over the full 30-year term, that adds up to $446,406 in total interest — more than the original loan amount. Early payments are mostly interest because the formula charges interest on the full remaining balance every month; as the balance shrinks, more of each fixed payment goes toward principal even though the payment itself never changes. This front-loading is normal for every amortizing loan, not a sign anything is wrong with the calculation.
US Income Tax Calculator
Data source
Data source: federal withholding methodology follows IRS Publication 15-T, and bracket thresholds are taken from the IRS's published federal income tax rates and brackets.
Tax year
Tax year: 2024 and 2025 federal brackets are both supported; figures are reviewed and updated every January.
Known limitations
Limitations: this calculator does not model the Alternative Minimum Tax (AMT), investment income (capital gains or dividends), self-employment tax, or tax credits such as the Child Tax Credit or Earned Income Tax Credit. It assumes ordinary W-2 employment income with either the standard or a manually entered itemized deduction.
Worked example
Take $85,000 in gross income, single filer, 2024, taking the standard deduction. Taxable income is $85,000 − $14,600 = $70,400. The IRS taxes that amount one bracket at a time, from the bottom up:
10% on first $11,600 = $1,160
12% on $11,600–$47,150 ($35,550) = $4,266
22% on $47,150–$70,400 ($23,250) = $5,115
Total federal tax = $10,541
That works out to an effective rate of 12.4% ($10,541 ÷ $85,000), even though the marginal rate is 22%. The two numbers describe different things: the marginal rate is the rate on your next dollar of income, while the effective rate blends every bracket you passed through along the way. It's a common point of confusion — people sometimes assume their whole income is taxed at their top bracket, but only the income inside that bracket actually is.
Canadian Income Tax Calculator
Data source
Data source: federal and provincial tax brackets, basic personal amounts, and CPP/EI rates and thresholds are taken from the Canada Revenue Agency's T4032 Payroll Deductions Tables published on canada.ca.
Tax year
Tax year: 2024 federal and provincial brackets; figures are reviewed and updated every January.
Known limitations
Limitations: this calculator models employment income only. It does not account for capital gains, dividend income and the dividend tax credit, or Quebec's separate provincial filing system and federal abatement with full precision — Quebec results should be treated as a rough estimate rather than an exact figure.
Worked example
Take $70,000 in employment income, Ontario, no RRSP contribution. Federal taxable income is $70,000 − $15,705 (federal basic personal amount) = $54,295. Since that's below the first federal bracket ceiling of $55,867, the entire amount is taxed at the lowest 15% federal rate. Ontario taxable income is $70,000 − $12,399 (Ontario's own basic personal amount) = $57,601, which spans two provincial brackets:
Federal: 15% on $54,295 = $8,144.25
Ontario: 5.05% on first $51,446 = $2,598.02
Ontario: 9.15% on remaining $6,155 = $563.18
CPP: $65,000 (capped) × 5.95% = $3,867.50
EI: $63,200 (capped) × 1.66% = $1,049.12
Note that CPP is calculated on $65,000, not $66,500 — because $70,000 exceeds the $68,500 maximum pensionable earnings for 2024, contributions stop accruing above that cap. EI works the same way: insurable earnings are capped at $63,200, so the $70,000 income never gets taxed for EI on its last $6,800. After federal tax, provincial tax, CPP, and EI, net income comes to $53,777.92. Quebec residents would see different numbers here for two reasons: Quebec collects its own provincial tax through Revenu Québec rather than using these CRA-administered brackets, and federal tax is reduced by a 16.5% Quebec abatement to account for that separate system. Quebec also runs its own QPP instead of CPP, at a slightly different rate.
Auto Loan Calculator
Formula
Formula: the same standard amortizing-loan PMT formula used by the mortgage calculator, applied to the amount financed (vehicle price, minus down payment and trade-in value, plus any sales tax rolled into the loan).
M = P × [r(1+r)n] / [(1+r)n − 1]
Data source
Sales tax rates: average combined state and local sales tax rates come from the Tax Foundation's state sales tax data.
Known limitations
Limitations: this calculator does not model dealer fees, documentation fees, GAP insurance, extended warranties, or other dealer add-ons that commonly get rolled into a real-world auto loan. Sales tax is a state average and may not reflect your specific city or county rate.
Worked example
Take a $28,000 vehicle, $3,000 down, 60 months, 5.9% APR, no trade-in. The amount financed is $28,000 − $3,000 = $25,000, and the monthly rate is r = 0.059 ÷ 12 = 0.004917.
M = 25,000 × [0.004917 × (1.004917)60] / [(1.004917)60 − 1] = $482.16/month
Total interest over 60 months comes to $3,930. Stretching the same loan to 72 months drops the monthly payment to $413.14 but raises total interest to $4,746 — about $69 less per month, but $817 more in interest over the life of the loan. The lower payment can make sense if it keeps you within budget, but it's not free money: every extra month of term is extra time for interest to accrue on a slowly-shrinking balance.
How to report a data error
If you find a bracket, rate, or threshold that looks out of date or incorrect, please contact us with the calculator name and the figure you think is wrong. We commit to verifying and fixing any confirmed data error within 7 days.
Contact usHow we test our calculations
Every formula on this site is checked against more than just my own arithmetic before it ships. Each calculator is cross-referenced against an official government tool where one exists — the IRS Tax Withholding Estimator for the US income tax calculator, and the CRA's online payroll deductions calculator for the Canadian one — to confirm brackets, exemptions, and caps are applied the same way. Where no government tool covers the exact scenario, like a full mortgage amortization schedule or an auto loan with a trade-in and sales tax rolled in, I cross-check results against established third-party calculators like Bankrate to confirm the math lines up within rounding. A handful of known test cases — specific inputs with manually verified expected outputs — are documented directly in the codebase and re-run any time the underlying formulas change, so a future edit can't silently break a calculation that used to be correct. That process catches most issues before a calculator ever goes live, but it isn't infallible. If you find a result that looks wrong, the contact page is the fastest way to flag it: verified errors get fixed within 7 days, and meaningful data fixes get noted by updating this page's underlying tax year and the calculators it covers.