Mortgage and auto loan calculators
The mortgage and auto loan tools use a standard fixed-rate amortization model. In plain language, the monthly payment is calculated from three main inputs: the financed amount, the monthly interest rate, and the number of payments.
M = P × [r(1 + r)n] / [(1 + r)n - 1]
P is the loan principal, r is the annual rate expressed as a decimal and divided by 12, and n is the total number of monthly payments. When the annual rate is 0%, M equals P divided by n.
The mortgage principal is home price minus down payment. The auto-loan principal is vehicle price minus down payment. Total paid is the unrounded monthly payment multiplied by n, and total interest is total paid minus P.
This formula is useful because it lets readers compare how rate, term, and down payment change the result. It does not automatically include taxes, insurance, HOA dues, registration, dealer add-ons, or lender-specific fees.
Savings calculator: APY-consistent monthly growth
The savings input is APY, which already reflects compounding across a full year. To avoid overstating growth, the calculator converts APY to an equivalent monthly rate rather than dividing APY by 12.
i = (1 + APY)1/12 - 1
FV = B(1 + i)n + C × [((1 + i)n - 1) / i]
APY is expressed as a decimal; B is the starting balance, C is the end-of-month deposit, i is the APY-equivalent monthly rate, and n is the number of months.
For example, the savings calculator's default inputs are a $4,000 starting balance, $250 monthly deposits, 4.3% APY, and 120 months. The unrounded result is $43,331.76, displayed as $43,332: $34,000 of deposits and $9,332 of interest.
Investment calculator: annual-effective return assumption
The investment field is a hypothetical annual return rather than a quoted savings APY, but it uses the same effective-annual conversion. The calculator finds the equivalent constant monthly rate so twelve modeled months compound to the entered annual assumption.
r = (1 + annual return)1/12 - 1
FV = B(1 + r)n + C × [((1 + r)n - 1) / r]
The annual return is expressed as a decimal. Contributions are added at the end of each month. When the modeled rate is 0%, both growth formulas reduce to FV = B + Cn.
This is a clean way to compare contribution levels, time horizons, and assumed returns. It is not a prediction engine and it does not attempt to model fluctuating rates, taxes, account fees, or contribution timing differences.
Calculation order, validation, and rounding
- Read numeric inputs and reject impossible or out-of-range combinations before showing a result.
- Convert the annual rate using the convention for that calculator: loan APR divided by 12, while savings APY and the investment annual-effective assumption use the twelfth-root formula.
- Run the amortization or monthly balance model at full available numeric precision.
- Round currency only for display: monthly loan payments show cents, while summary totals and growth balances show whole dollars.
Default-case verification values
| Calculator | Default inputs | Expected primary result |
|---|---|---|
| Mortgage | $420,000 price; $84,000 down; 6.4%; 30 years | $2,101.70 monthly principal and interest |
| Auto loan | $36,000 price; $6,000 down; 6.1%; 60 months | $581.38 monthly payment |
| Savings | $4,000 initial; $250 monthly; 4.3% APY; 10 years | $43,332 future balance |
| Investment | $10,000 initial; $400 monthly; 7%; 20 years | $241,711 projected balance |
What each calculator excludes on purpose
| Calculator | Main exclusions |
|---|---|
| Mortgage | Property tax, insurance, HOA dues, PMI, maintenance, utilities, closing costs. |
| Auto loan | Sales tax, title, registration, warranties, insurance, fuel, maintenance, parking. |
| Savings | Taxes on interest, changing APYs, irregular deposits, fees, withdrawals. |
| Investment | Taxes, account fees, market volatility, asset allocation changes, employer match rules, withdrawals. |
When a simplified model fits the question
Use these calculators to compare controlled scenarios: one rate versus another, a shorter term versus a longer term, or one recurring contribution versus another. Do not use a simplified output as a lender quote, account statement, tax calculation, or prediction of market performance.
The purpose of the methodology page is not to claim precision where precision is impossible. It is to show the assumptions clearly enough that a reader can decide whether the estimate is good enough for the question they are asking.
A result is suitable for an early planning comparison only when the excluded items are either irrelevant to that comparison or added separately. For a commitment or regulated disclosure, use figures from the relevant lender, financial institution, account provider, or qualified professional.
Common interpretation errors
- Treating APR, APY, and an assumed investment return as interchangeable rate labels.
- Trying to reproduce a result from a rounded monthly payment instead of the full-precision calculation.
- Comparing a principal-and-interest loan result with an all-in quote that contains taxes, insurance, or fees.
- Reading a constant-return investment projection as a probable ending balance rather than one hypothetical scenario.
How to reproduce or question a result
- Record every input exactly, including the selected term and whether a rate is APR, APY, or an assumed return.
- Compare against the full-precision formula before rounding to the displayed number of decimal places.
- If a result still differs, use the contact page and include the calculator URL, all inputs, expected output, and observed output.
Methodology questions
Both are treated as effective annual rates. Each calculator uses (1 + annual rate)^(1/12) - 1 so twelve modeled months compound to the entered annual rate.
No. Calculations retain the available numeric precision during the model and round only the values shown on the page.
They are added at the end of each modeled month, after that month's growth is applied to the existing balance.
Sources used alongside the formulas
Formulas provide structure, but consumer finance decisions also depend on terms, fees, and assumptions. The trusted sources page lists outside references used to keep those explanations grounded.
Choose the model that matches the decision
Use the mortgage calculator or auto-loan calculator for fixed-payment financing comparisons. Use the savings calculator for a quoted APY and the investment calculator for a range of hypothetical market-return assumptions. The rate label and the omitted real-world costs are part of the result, not fine print to ignore.