Our Methodology
Every calculator on this site uses standard, documented financial mathematics. This page shows the exact formulas, what they assume, and where they come from, so you can verify any result yourself.
How to Read This Page
Each entry below lists the formula a calculator uses, the variables involved, and the assumptions behind it. The formulas are not proprietary: they are the same financial mathematics used by lenders, banks, and spreadsheet functions like PMT, FV, and PV. If a result from one of our tools ever disagrees with your lender's figure, the difference will come from inputs (fees, rounding conventions, payment timing), not from different math, and the notes explain where those differences can appear.
Calculations run entirely in your browser. We never see, store, or transmit the numbers you enter.
Amortized Loan Payment
M = P × [ r(1 + r)^n ] / [ (1 + r)^n − 1 ]- M = monthly payment
- P = loan principal
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of monthly payments
This is the standard amortization formula used by lenders in the United States and most other markets. Amortization schedules apply each payment first to interest accrued that month, with the remainder reducing principal. Our mortgage calculator adds monthly escrow items (property tax, insurance, PMI) as annual amounts divided by 12; escrow items do not affect the amortization itself.
Compound Growth with Regular Contributions
FV = P(1 + r/k)^(kt) + PMT × [ ((1 + r/k)^(kt) − 1) / (r/k) ]- FV = future value
- P = starting principal
- PMT = contribution per compounding period
- r = annual rate as a decimal
- k = compounding periods per year
- t = years
The first term grows the starting balance; the second is the future value of an ordinary annuity (contributions made at the end of each period). Results assume a constant rate and regular contributions. Real investment returns vary year to year, so projections are estimates, not guarantees.
Future Value and Present Value
FV = PV × (1 + r)^n and PV = FV / (1 + r)^n- FV = future value
- PV = present value
- r = rate per period as a decimal
- n = number of periods
These are the time value of money identities that underpin most finance. The inflation calculator uses the same math with the inflation rate in place of a return, showing what future amount matches the purchasing power of money today.
Compound Annual Growth Rate (CAGR)
CAGR = (Ending Value / Beginning Value)^(1/years) − 1- Values must both be positive
- years = the holding period in years (fractions allowed)
CAGR is the constant annual rate that would take the beginning value to the ending value over the period. It smooths out volatility and says nothing about the path in between.
Return on Investment (ROI)
ROI = (Net Profit / Total Cost) × 100 Annualized: (1 + ROI)^(1/years) − 1- Net profit = final value minus total invested, including fees and costs
Simple ROI ignores time, so we also report the annualized figure for comparisons between investments held for different periods.
Annual Percentage Rate (APR)
APR is the rate that makes the present value of all payments equal the amount financed net of fees- Solved iteratively (there is no closed form)
- Amount financed = principal minus upfront fees and points
This matches the Regulation Z (Truth in Lending Act) approach that United States lenders must use in disclosures. Our calculator solves for the rate numerically, the same way lender software does. See the Consumer Financial Protection Bureau for the regulatory definition.
Debt Payoff (Avalanche and Snowball)
Month by month simulation: interest = balance × (APR/12), then payment reduces balance- Avalanche: extra payment goes to the highest APR debt first
- Snowball: extra payment goes to the smallest balance first
Payoff dates and total interest come from simulating every month until each balance reaches zero, not from an approximation. Avalanche always minimizes total interest; snowball trades some interest for earlier debt eliminations.
Loan to Value (LTV)
LTV = (Loan Amount / Appraised Property Value) × 100- CLTV adds all loans secured by the property to the numerator
Lenders use LTV thresholds for pricing and mortgage insurance requirements. Conventional loans typically require PMI above 80% LTV.
Sources and Standards
- Consumer Financial Protection Bureau (consumerfinance.gov) for APR and mortgage disclosure rules under Regulation Z.
- IRS publications for contribution limits and tax-adjacent figures referenced in educational content.
- Standard time value of money mathematics as published in any corporate finance text and implemented in spreadsheet functions (PMT, FV, PV, RATE).
Limitations
Our tools produce estimates for planning and comparison. They assume constant rates, regular payments, and no missed or extra payments unless a tool models them explicitly. Lenders may round differently, charge fees we cannot know in advance, or use day-count conventions that shift figures slightly.
Nothing on this site is financial advice. For decisions involving significant money, confirm figures with your lender, plan documents, or a licensed professional. See our disclaimer for details.