Calculation methodology

Mortgage payment

The mortgage payment calculator models a conventional fixed-rate loan. The original principal is the home price minus the down payment. For principal P, monthly rate r (the entered annual nominal rate divided by 12), and n monthly payments, scheduled monthly principal and interest is:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

The underlying model uses M = P / n when the rate is zero, although the calculator interface requires a positive mortgage rate.

A month-by-month amortization schedule calculates interest from the opening balance, applies scheduled principal, then applies configured extra principal without allowing the balance to become negative. The regular payment does not recast after an extra payment; instead, the modeled payoff period shortens. The final payment is capped at the amount owed.

Housing-cost assumptions

• The first-month housing estimate adds principal and interest, monthly property tax, homeowners insurance, homeowners association fees, and applicable private mortgage insurance (PMI).
• Percentage-based property tax uses the original home price and remains level. Insurance and homeowners association fees also remain level; future escrow changes are not forecast.
• Monthly PMI is estimated as the opening loan balance multiplied by the annual PMI rate and divided by 12. It stops when the scheduled closing balance reaches the user-entered percentage of the original home value.
• Appreciation, lender seasoning rules, automatic-cancellation laws, and appraisal requirements are not modeled.
• Closing costs contribute to estimated cash needed but are not financed or added to principal. Entered seller credits reduce those closing costs, but do not reduce the sale price, down payment, principal, or scheduled payment. This model limits seller credits to the entered closing costs.

Mortgage affordability

The mortgage affordability calculator estimates a comfortable range and an upper limit; it does not determine approval. If I is gross monthly income, D is existing monthly debt, and F and B are the selected front-end and back-end debt-to-income (DTI) ratios, the housing budget is:

front-end limit = I * F
back-end limit = I * B - D
housing budget = max(0, min(front-end limit, back-end limit))

The model runs at the low and high comfortable front-end targets with the comfortable back-end target, then at the maximum targets for the estimated upper limit. These targets are editable educational rules of thumb, not underwriting criteria.

Because taxes, insurance, maintenance, PMI, closing costs, and down payment can all depend on home price, the calculator uses a bounded binary search. At each candidate price, it deducts closing costs from available cash, caps the down payment at 20% of the price, derives principal, converts the annual maintenance percentage to a monthly allowance, and compares the initial total housing cost with the DTI budget. The search stops within $1 of price precision or at its documented iteration limit.

The result identifies whether available cash, front-end DTI, or back-end DTI is the binding modeled constraint. Location-specific costs, lender overlays, credit history, ordinary living expenses, and loan-program eligibility are not modeled.

Compound interest

The compound interest calculator isolates the growth of one principal with no deposits or withdrawals. For initial principal P, nominal annual rate r, m compounding periods per year, and time t in years:

A = P * (1 + r / m)^(m * t)
APY = (1 + r / m)^m - 1

The calculator supports annual, semiannual, quarterly, monthly, and daily compounding. Time is entered in years and months. It compounds for whole periods and applies prorated simple interest to a final partial period. A zero rate leaves principal unchanged; supported negative rates reduce it. Real financial products may use different accrual and day-count conventions.

Doubling time is shown only for positive rates and uses the exact logarithmic solution for the selected compounding frequency.

Investment returns

The investment returns calculator performs a monthly simulation for conservative, expected, and optimistic constant-return scenarios. The outer scenarios are illustrative differences, not confidence intervals or predictions.

Annual effective assumptions are converted to monthly rates:

monthly gross return = (1 + annual return)^(1 / 12) - 1
monthly fee rate = (1 + annual fee)^(1 / 12) - 1
monthly inflation rate = (1 + annual inflation)^(1 / 12) - 1

Each month, the model applies events in this order:

1. Add a beginning-of-period contribution when selected.
2. Apply gross gain or loss to the opening investable balance.
3. Deduct the monthly fee from the balance after gross growth.
4. Add an end-of-period contribution when selected.
5. Deduct scheduled recurring and one-time withdrawals.
6. Floor the balance at zero and record any unfunded withdrawal.

For a gross withdrawal, the model treats the entered amount as the requested account distribution and estimates after-tax cash as funded withdrawal * (1 - withdrawal tax rate). For an after-tax cash request, it grosses up the requested distribution as cash requested / (1 - withdrawal tax rate). Withdrawal tax applies only to the amount the modeled balance can fund.

The simplified terminal tax estimate is min(pre-tax ending balance, max(0, cumulative gross growth - cumulative fees) * entered tax rate). It is deducted once after the final projection month. It is not a tax-return calculation and does not model actual cost basis, realization timing, holding periods, dividends, capital-gain distributions, loss offsets, tax brackets, account type, or taxes associated with earlier withdrawals.

Fees apply to modeled assets whether the month's return is positive or negative. Contribution increases take effect every 12 months. At month k, the inflation-adjusted balance is the nominal balance divided by (1 + monthly inflation rate)^k.

Shared conventions and limitations

• Inputs and calculations use US conventions and US dollar formatting.
• Calculations retain floating-point precision internally. Values are rounded for display; mortgage schedules include a final-payment adjustment and never compare a balance directly with zero.
• Displayed precision is not a promise of real-world accuracy. Taxes, fees, rates, and market outcomes can change.
• Inputs are user supplied. The site does not quote live mortgage or investment rates.
• Share URLs are created only after an explicit Share action and CSV exports preserve enough precision to reconcile modeled totals.
• Models exclude adjustable-rate and government-backed mortgages, lender underwriting, real-time market data, and personalized tax treatment.

The formulas, terminology, and test fixtures require content review before public launch.