Methodology
Last updated: July 26, 2026
Most financial websites ask you to trust their numbers. We'd rather show you the math. This page documents every formula that powers our calculators, along with the assumptions behind each default value. If you can follow high-school algebra, you can verify everything we publish.
Our Methodology
Each FinCalc Hub calculator follows three principles:
- Open formulas. The equation is shown on the page, not hidden in code.
- Stated assumptions. Every default value (rate, tax, inflation) is displayed and editable.
- Reproducible results. You can recompute any output by hand from the inputs and the formula below.
Core Formulas
1. Mortgage & loan monthly payment (amortization)
The fixed monthly payment M that pays off a loan of principal P at monthly interest rate r over n months:
M = P · [ r(1 + r)n ] / [ (1 + r)n − 1 ]
Where r is the annual rate divided by 12, and n is the loan term in years times 12. This is the standard amortization identity used by every U.S. fixed-rate mortgage and most installment loans. Our Mortgage Calculator, Loan Calculator, and Auto Loan Calculator all use it.
2. Compound interest
The future value A of a principal P compounded n times per year at rate r for t years:
A = P · (1 + r/n)n·t
For monthly contributions C made at the end of each period, add the future value of an ordinary annuity:
A = P · (1 + r/n)n·t + C · [ ((1 + r/n)n·t − 1) / (r/n) ]
Used by the Compound Interest Calculator and Savings Goal Calculator.
3. APR vs interest rate
The interest rate is the cost of borrowing the principal. The APR (Annual Percentage Rate) bundles in certain upfront fees, giving a truer cost of credit. APR is defined and regulated under U.S. Regulation Z (Truth in Lending). Roughly:
APR ≈ (total finance charges including fees) / (loan amount) / (term in years)
The exact APR is found by solving for the rate that equates the loan amount to the present value of all scheduled payments plus fees. See our APR Calculator.
4. ROI and CAGR
Simple return on investment:
ROI = (Final Value − Initial Value) / Initial Value
Compound annual growth rate, which annualizes ROI over t years:
CAGR = (Final Value / Initial Value)1/t − 1
Used by the ROI Calculator and Investment Calculator.
5. Retirement nest-egg withdrawal (4% rule baseline)
Our Retirement Calculator projects a portfolio's value by compounding contributions forward, then models withdrawals. The widely cited 4% rule (Bengen, 1994) suggests first-year withdrawals of ~4% of the portfolio, inflation-adjusted thereafter, as a baseline for a 30-year retirement. We use it as a default assumption only — users can change the withdrawal rate.
6. Present value & loan balance
To find the remaining balance B after k payments of an amortizing loan:
B = P · (1 + r)k − M · [ ((1 + r)k − 1) / r ]
This drives the amortization schedules shown in our loan and mortgage calculators.
Default Values & Data Sources
When a calculator needs an input the user hasn't supplied, we use a clearly labeled default. Defaults are chosen to reflect a reasonable recent U.S. average and are updated periodically. Current defaults include:
| Assumption | Typical default | Basis |
|---|---|---|
| Mortgage rate | ~6.5% | 30-year fixed U.S. average, Freddie Mac PMMS |
| Auto loan rate | ~7.0% | 5-year new-car average, Experian State of the Auto Finance Market |
| Inflation | 3% | Long-run U.S. CPI average, U.S. Bureau of Labor Statistics |
| Investment return | 6–8% | Historical nominal S&P 500 average minus typical inflation |
| Retirement withdrawal | 4% | Bengen (1994), 4% rule |
Every default is shown on its calculator's page and can be overridden by the user. We do not store any of the numbers you enter — all calculations run in your browser. See our Privacy Policy.
Limitations
No calculator can capture every real-world factor. Be aware of the following:
- Taxes and insurance. Our mortgage calculator shows principal and interest only; real monthly payments usually also include property tax, homeowners insurance, and PMI, which vary by location and loan.
- Variable rates. Formulas above assume a fixed rate. ARMs and credit cards with changing rates produce different results over time.
- Market volatility. Investment and retirement projections assume a constant average return. Real returns are uneven and can be negative for years at a time.
- Local rules. Tax brackets, contribution limits, and lending rules differ by jurisdiction. Our defaults reflect U.S. norms.
Use our calculators as a starting point, not the final word. For decisions that matter, confirm the numbers with a qualified professional.
Verification & Testing
Every calculator ships with an automated numerical test suite (currently 27 scenarios) that checks outputs against hand-computed values and published reference figures. If a future code change breaks a formula, the build fails before it reaches this site.
Questions about our math? Get in touch — we're happy to walk through any formula. Also see our Editorial Policy for how content is created and updated.