Methodology

Transparency is core to our mission. This page documents the standard financial formulas and assumptions used across our calculators. Every formula here is a well-established time-value-of-money convention used in consumer finance; nothing is proprietary or opaque.

General conventions

• Currency. All amounts are displayed in U.S. dollars (USD), rounded to the nearest cent for display. Internal calculations use full precision and round only at the final step.
• Interest rates. Annual rates are converted to monthly by dividing by 12. This is the standard convention for consumer loans and mortgages.
• Compounding. Unless otherwise noted, interest compounds monthly, matching how most savings, loan, and credit accounts accrue in practice.
• Client-side calculation. All math runs in your browser. We do not transmit your inputs to any server.

Loan and mortgage calculations

Mortgage, personal loan, and auto loan calculators use the standard amortization formula:

M = P × [ r(1+r)ⁿ ] ÷ [ (1+r)ⁿ − 1 ]

• M = monthly payment
• P = principal (amount borrowed)
• r = monthly interest rate (annual rate ÷ 12 ÷ 100)
• n = total number of monthly payments

For interest-free loans (r = 0), the payment simplifies to P ÷ n. Total interest is calculated as (M × n) − P. The amortization schedule is generated iteratively: each month, interest = balance × r, principal = payment − interest, and the new balance = previous balance − principal.

What we exclude: Mortgage and auto loan calculators show principal and interest only. Property taxes, homeowners insurance, PMI, HOA dues, registration, and dealer fees are not included unless you add them to the price yourself.

Compound interest and future value

The future value of a present sum uses the compound interest formula:

FV = PV × (1 + r/n)^n×t

The future value of a series of regular contributions (an ordinary annuity) uses:

FV = PMT × [ (1+r)ⁿ − 1 ] ÷ r

Where PMT is the contribution per period, r is the periodic rate, and n is the number of periods. Contributions are assumed to occur at the end of each period (ordinary annuity convention). Total interest earned = projected balance − total amount contributed.

Retirement projections

The retirement calculator projects your nest egg by combining the compound growth of current savings with the future value of ongoing monthly contributions. Estimated monthly retirement income is then derived using a withdrawal rate (default 4%, adjustable):

Monthly income = (nest egg × withdrawal rate) ÷ 12

The 4% guideline originates from the "Trinity study," which found that withdrawing 4% of a starting balance in year one (then adjusting for inflation) had a high probability of lasting 30 years across historical market conditions. For retirements longer than 30 years, a more conservative 3–3.5% rate is recommended.

Return on investment (ROI) and CAGR

Total return on investment:

ROI = (Final Value − Initial Cost) ÷ Initial Cost × 100%

Annualized return (Compound Annual Growth Rate, CAGR):

CAGR = (Final ÷ Initial)^{(1 ÷ years)} − 1

For accurate real-world results, include reinvested dividends in the final value and subtract fees, commissions, and taxes from your proceeds. To compare against purchasing power, subtract inflation from your nominal return.

Credit card payoff

Credit card payoff is computed iteratively because the closed-form solution becomes numerically unstable at high interest rates. Each month:

• Interest = balance × (APR ÷ 12 ÷ 100)
• Principal reduction = payment − interest
• New balance = previous balance − principal reduction

The loop continues until the balance reaches zero. If the payment does not exceed the monthly interest, the debt never repays and the calculator warns you. Total interest is the sum of all monthly interest charges.

Savings goal

The savings goal calculator solves the annuity formula for the required contribution. First, it projects the future value of current savings; the remaining gap is divided across monthly contributions:

PMT = gap × r ÷ [ (1+r)ⁿ − 1 ]

Where gap = target − future value of current savings. If the return rate is 0%, the contribution is simply gap ÷ number of months.

Budget planner (50/30/20 rule)

The 50/30/20 rule allocates after-tax income as 50% needs, 30% wants, and 20% savings. The framework was popularized by Elizabeth Warren and Amelia Warren Tyagi in "All Your Worth: The Ultimate Lifetime Money Plan." The calculator applies fixed percentages to the after-tax income you enter.

Net worth

Net worth = total assets − total liabilities. The calculator sums the asset and liability values you enter and subtracts. It performs no estimation or projection; accuracy depends entirely on the values you provide. For real-world accuracy, use current account balances, realistic market values for property and vehicles (e.g., comparable sales, Kelley Blue Book), and current payoff amounts for all loans.

Assumptions and limitations

• Rates are assumed constant over the full term. Real loans may have variable rates.
• Contributions are assumed regular and constant. Real incomes and expenses fluctuate.
• Tax effects are not modeled. Investment returns in taxable accounts are reduced by taxes; tax-advantaged accounts are not.
• Inflation is not automatically applied. Use a real (after-inflation) rate, or interpret nominal results accordingly.
• All results are educational estimates, not guarantees or professional advice.