Balance & Equity Over Time
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Payment Composition
Key Milestones
Cost Breakdown
Cumulative Interest
Equity Build-Up (%)
Amortization Schedule
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Refinance Analysis
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Calculate your monthly mortgage payment and view a full amortization schedule. Compare loan scenarios side by side. Check if refinancing makes sense. Model compound interest on savings or investments. Go deeper with Monte Carlo simulation to see the full range of possible outcomes.
Monthly payment, amortization schedule, extra payment savings, side-by-side comparison of up to 3 loan scenarios. Works for mortgages, auto loans, student loans, and more.
Compare renting and investing the difference vs buying with a mortgage. Includes property tax, insurance, and maintenance. Plus a refinance break-even calculator.
Compound interest calculator for CDs and savings accounts. Monte Carlo simulation for stocks and crypto. Goal-seeking mode: find how much to save monthly to reach your target.
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Mortgage Calculator & Amortization Schedule — Enter your loan amount, rate, and term to see your monthly payment and a full amortization schedule. View how much of each payment goes to principal vs interest. Add extra payments to see how much interest you save and how many months you cut off the loan. Compare 15-year vs 30-year mortgages, or any other scenarios side by side.
Rent vs Buy Calculator — Not sure whether to rent or buy? CalcMonte compares the true cost of homeownership (mortgage, property tax, insurance, maintenance, PMI, HOA) against renting and investing the difference. Uses Monte Carlo simulation to show the probability of buying winning vs renting over any time horizon.
Mortgage Refinance Calculator — See if refinancing makes sense. Enter your new rate and closing costs to find the break-even month, monthly savings, and total interest saved over the life of the loan.
Home Price Volatility & Underwater Risk — Most mortgage calculators assume your home goes up in value every year. CalcMonte lets you add price volatility and see the probability of your home dropping below the loan balance — the underwater risk that other tools don't show.
Compound Interest & Savings Calculator — Calculate compound interest for CDs, savings accounts, or any fixed-rate investment. Set volatility to 0% for a simple deterministic projection, or add volatility to see the range of possible outcomes using Monte Carlo simulation.
Investment Simulator with Monte Carlo — Simulate S&P 500, NASDAQ, bond funds, or any custom asset with realistic volatility. See percentile bands from 5th to 95th showing best-case to worst-case outcomes. Add monthly contributions and one-time events.
Goal-Seeking Mode — How much do you need to save per month to reach $1,000,000? CalcMonte finds the answer by running Monte Carlo simulations at any confidence level you choose.
Full Housing Cost Analysis — Go beyond just principal and interest. Add property tax, homeowner's insurance, maintenance costs, PMI, and HOA fees to see your true monthly housing cost.
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This page documents the mathematical models, formulas, and assumptions that power both the Loan Analytics and Asset Simulator modules. Every calculation runs client-side in your browser — no data is sent anywhere.
The periodic payment for a fixed-rate fully-amortizing loan is computed using the standard annuity formula:
Each payment is split into an interest component and a principal component. The interest portion for period k is the outstanding balance multiplied by the periodic rate. The principal portion is the remainder:
Extra payments are added directly to the principal portion each period, which reduces the outstanding balance faster and shortens the loan term. The principal-interest crossover occurs at the period where the principal portion first exceeds the interest portion — a milestone that depends on the rate, term, and extra payment amount.
The Asset Simulator supports six compounding modes. The future value after time t depends on the compounding frequency:
Continuous compounding represents the mathematical limit as n approaches infinity. In practice, the difference between daily and continuous compounding is usually small for typical annual return assumptions, but the continuous formula is analytically cleaner and connects naturally to the GBM stochastic model.
Deterministic vs. stochastic modes: When annual volatility is greater than 0%, the simulator switches to a monthly-step GBM model; the compounding selector applies only to deterministic projections.
When volatility is non-zero, the Asset Simulator models price dynamics using Geometric Brownian Motion — the same framework underlying the Black-Scholes option pricing model. The stochastic differential equation is:
For simulation, we discretize this into monthly time steps using the exact solution:
The drift-adjustment term is the Itô correction. It ensures that the expected value of the GBM process equals the deterministic growth path. Without this correction, volatility would systematically inflate the expected outcome due to the asymmetry of log-normal distributions.
The simulator generates multiple independent GBM paths (configurable, default 500). Each path is a sequence of monthly values obtained by repeatedly applying the discretized GBM step. Cash flows (contributions, withdrawals, one-time events) are applied after the growth step each month.
Random numbers are generated using the Box-Muller transform, which converts pairs of uniform random variables into standard normal random variables:
At each monthly time step, the values from all simulation paths are sorted and percentiles are extracted using order statistics. For N paths and percentile q, the value is taken at index . The displayed bands are the 5th, 10th, 25th, 50th (median), 75th, 90th, and 95th percentiles.
The final-value distribution histogram bins all terminal values across paths. The probability analysis computes the empirical probability of exceeding specific return thresholds by counting the fraction of paths above each target.
Constant volatility: GBM assumes volatility (σ) is constant over time. Real markets exhibit volatility clustering — periods of high volatility tend to follow other high-volatility periods (GARCH effects). GBM underestimates the frequency of extreme events.
Log-normal returns: GBM produces log-normally distributed returns. Real financial returns have fatter tails than the log-normal distribution predicts. This means crashes of the magnitude seen in 2008 or 2020 are more likely than the model suggests.
No mean reversion: The model does not incorporate mean reversion — the tendency of valuations to return to historical averages over long periods. This is most relevant for very long simulation horizons (20+ years).
Fixed rates: Loan calculations assume a fixed interest rate for the entire term. In practice, adjustable-rate mortgages (ARMs) and refinancing opportunities can significantly alter outcomes.
Loan timeline display: For non-monthly payment schedules such as weekly, bi-weekly, and semi-monthly, the amortization calculation uses the exact payment frequency, but charts, milestones, and some summaries are displayed on rounded month labels for readability and alignment with the monthly asset overlays.
No taxes or fees: The simulator does not account for capital gains taxes, dividend taxes, management fees, inflation, or transaction costs, all of which reduce real returns. A 10% nominal return might be 6-7% after taxes and fees.
Monthly granularity: All simulations use monthly time steps (Δt = 1/12). For very high volatility assets, finer granularity could yield different percentile estimates, though the expected values remain unbiased due to the Itô correction. One-time events are scheduled by integer month on this monthly timeline.
Cash flow timing: Contributions and withdrawals are applied at the end of each monthly step (post-growth). Monthly recurring cash flows are modeled directly; non-monthly recurring choices such as bi-weekly are mapped into the monthly simulation timeline as an approximation. Withdrawals are capped at the available balance to prevent negative values.