Our Methodology

Every result on CalcPrimeHQ comes from documented, reproducible math. This page collects the formulas and conventions our calculators use.

Core loan mathematics

Amortizing payment

PMT = L × r ÷ (1 − (1 + r)−n)

Where L is principal, r = APR ÷ 12 ÷ 100 is the monthly rate, and n is the payment count. Zero-rate loans divide principal evenly. Used by: auto loan, personal loan, mortgage payment, amortization, refinance, consolidation.

Schedule simulation

Rather than shortcut formulas, loan calculators simulate each month: interest accrues on the outstanding balance (balance × r), the remainder of the fixed payment reduces principal, and totals accumulate from real iterations. Extra-payment scenarios re-run the identical loop with a larger payment.

Fixed-payment revolving payoff

Credit card and debt-payoff tools apply Balance(m+1) = Balance(m) × (1+r) − Payment, iterating up to 1,200 months. When payment ≤ monthly interest, results flag the situation rather than returning misleading values.

Debt snowball / avalanche simulation

Each month: interest accrues on all live debts; minimum payments apply; the entire spare budget targets the strategy-ordered debt (smallest balance for snowball, highest APR for avalanche). Paid-off debts’ minimums roll into the following month’s budget automatically.

Growth mathematics

Future value with contributions

FV = P(1+i)n + C × [((1+i)n − 1) ÷ i]

Contributions assumed at month-end. Monthly compounding divides annual rates evenly across periods; annual option compounds once per year after twelve deposits.

Required contribution (goal solving)

Inverting FV algebraically: C = (Goal − PV(1+i)n) × i ÷ ((1+i)n − 1). Returns zero when existing balance already reaches target.

CAGR and ROI

CAGR = (End/Begin)1/years − 1. Annualized ROI uses the same geometric convention. Total ROI divides net gain by total invested capital including fees.

Dollar-cost averaging

Buys shares monthly along an assumed smooth price trend; average cost equals invested dollars divided by accumulated shares. Lump-sum comparison invests equal cash at the initial price.

Mortgage specifics

  • PMI: flat 0.46% of original loan annually while LTV > 80% (adjustable input where relevant).
  • Property tax: user-entered annual amount, defaulting to ~0.9% of price when derived from rate.
  • Affordability solver: binary search over price for the largest loan whose P&I + tax + PMI fits the DTI-limited budget at 28% / 36% / 43% ceilings.
  • Rent vs buy: month-by-month wealth comparison — buyer equity (appreciation minus selling costs) versus renter portfolio (upfront costs plus monthly differences invested at the chosen return).

Lease mathematics

Standard closed-end lease model: depreciation = (net cap cost − residual) ÷ term; rent charge = (net cap cost + residual) × money factor; money factor = APR ÷ 2400; sales tax applied per payment.

Rounding and display

Internal computation runs at full float precision. Display rounds for readability only. Currency figures use U.S.-style formatting; percentages typically two decimals.

Known limitations

  • Constant-return assumptions replace real-world volatility.
  • Taxes on investment gains, inflation adjustments inside long projections, and escrow drift are simplified or excluded.
  • Lender-specific practices (fee structures, PMI cancellation rules, day-count conventions) may differ from these general models.

We document changes to methods on this page. Questions about any formula belong in our inbox.