Sumyard

Loan calculation methodology

The fixed-rate method used by Sumyard’s mortgage and car-loan calculators, with their assumptions, rounding and limitations. Other tools explain their own methods on their calculator pages.

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This page covers mortgage and car-loan calculations. Other calculators show their formula, reproducible example settings and assumptions beside the worksheet. Named references and dataset dates appear where a method or maintained snapshot needs them; a content update is not an independent professional review.

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Fixed-rate payment formula

For a loan principal P, monthly interest rate r, and n monthly payments, the principal-and-interest payment M is:

M = P × r ÷ (1 − (1 + r)−n)

The monthly rate is the annual interest rate divided by 12 and then by 100. Use the interest rate charged on the balance, not an APR that includes fees. At 0% interest, the payment is principal divided by the number of payments. Each monthly interest charge is calculated from the remaining balance; the rest of that month’s principal-and-interest payment reduces principal.

Mortgage assumptions

  • Principal equals home price minus the down payment.
  • Annual property tax and home insurance are each divided by 12 and added to the monthly principal-and-interest amount.
  • The interest rate is fixed and monthly payments are made on schedule.
  • The estimate excludes private mortgage insurance, HOA dues, closing costs, lender fees, points, changing taxes or insurance, and adjustable or balloon rates.

Car loan assumptions

  • Sales tax is calculated from vehicle price minus trade-in value, with the taxable amount floored at zero. This is a modeling assumption, not a local tax determination: some jurisdictions do not allow this trade-in credit.
  • Financed principal equals vehicle price plus sales tax, minus down payment and trade-in.
  • The interest rate is fixed and payments are made monthly on schedule.
  • The estimate excludes registration, title and documentation fees, rebates, add-ons, insurance and early-payment charges. It does not model outstanding trade-in debt or negative equity.

Rounding and currencies

Calculations retain full numeric precision internally; the final lender payment may differ because of currency rounding or payment dates. Loan durations are rounded to whole months. The annual interest rate divided by 12 is the monthly-rate convention for all currencies; daily-interest loans and other compounding conventions are not modeled. Displayed currency values are rounded for readability. Changing currency changes the symbol and number formatting only; it does not perform an exchange-rate conversion.

Validation and testing

The implementation has automated checks for a zero-interest loan, a standard 30-year mortgage and a car loan with financed sales tax. Input validation rejects non-positive principals or terms, negative interest rates and terms outside the calculator’s stated limits.

Reproduce a worked example

The mortgage guide walks through a $450,000 home with 20% down, a 6.5% annual interest rate and a 30-year term. The car guide walks through a $38,000 vehicle, a $5,000 down payment, 6% assumed sales tax and 7.2% interest over 60 months. Both guides also compare terms using the same principal and rate.

Example figures and comparison tables are generated using the same calculation functions as the interactive results. Automated tests check the example payments against independent expected values. The examples remain fixed in US dollars when the interactive inputs or display currency change.

Reading totals and dates

“Total of all payments” excludes the upfront down payment and trade-in. For a mortgage it includes the entered tax and insurance amounts across the full term, assuming they stay unchanged. The principal-and-interest bar excludes those extra costs. A payoff month assumes monthly payments begin one month from the current date; it is not a lender-provided due date. For a term ending partway through a year, the last balance point is the final payment rather than a full year-end.

Primary sources

Use and limitations

These results are estimates, not a loan offer or financial advice. Actual payments and borrowing costs depend on lender terms, fees, local taxes, insurance, timing and other contract details. Compare the calculator result with an official Loan Estimate or lender disclosure before making a decision.

Questions or corrections can be sent to contact@sumyard.app.