This page documents the formulas, regulatory definitions, and editorial review process behind our loan, savings, and investment tools. We use textbook financial mathematics and, where a calculator touches consumer-credit or tax rules, the relevant US regulation. International equivalents are noted so the figures remain comparable outside the United States.
All cash-flow calculators treat a dollar today as worth more than a dollar tomorrow. Future value is FV = PV(1 + r)^n, where r is the per-period rate and n is the number of periods. Present value inverts the same expression. This is the foundation for loan, savings, retirement, and bond-pricing tools.
Fixed-payment loan calculators use the ordinary annuity formula: P = L * r / (1 - (1 + r)^-n), where L is the loan principal, r the periodic interest rate, and n the total number of payments. Mortgage, auto, and personal-loan tools share this engine; only the rate-conversion step differs.
Savings and CD tools compound interest as A = P(1 + r/m)^(mt), with m compounding periods per year over t years. Continuous compounding uses A = Pe^(rt). The annual percentage yield (APY) reported by US banks follows Regulation DD: APY = (1 + r/m)^m - 1.
Our APR calculator follows the US Truth in Lending Act (Regulation Z, 12 CFR 1026), which defines APR as the rate that discounts all finance-charge cash flows back to the amount financed. We use the actuarial method described in Appendix J. The EU equivalent (APRC) under Directive 2008/48/EC uses the same underlying equation with different fee inclusions.
Where an options or warrant valuation is offered, we use the Black-Scholes-Merton closed-form solution for European options on non-dividend-paying stock: C = S*N(d1) - K*e^(-rt)*N(d2). Dividend-adjusted (Merton 1973) and put-call parity variants are noted in the calculator itself.
401(k), IRA, and HSA tools cap annual contributions at the limits published each year by the Internal Revenue Service. We refresh these limits within two weeks of the IRS Cost-of-Living Adjustment notice and tag the relevant calculators with the effective tax year.
Every finance calculator is reviewed against a worked example from an authoritative source (a CFPB consumer guide, an IRS publication, or a standard finance textbook such as Brealey, Myers and Allen). When the calculator output differs from the reference by more than rounding, we treat the discrepancy as a bug and fix the formula before publishing. Rates, contribution caps, and tax thresholds are dated and re-checked at least annually. The review date at the top of each calculator reflects the most recent verification.
