Calculation Methodology

Model version 1.0 · Published October 26, 2026. All amounts are in U.S. dollars. These tools estimate fully amortizing, fixed-rate loans with monthly payments. They do not model changing rates, late payments, defaults or regulatory APR.

The standard payment formula

• P: amount financed at the start of repayment.
• r: nominal annual interest percentage ÷ 100 ÷ 12.
• n: scheduled number of monthly payments.
• M: scheduled principal-and-interest payment before extra payments.

For example, 6% annual interest gives r = 0.005. The implementation uses log1p and expm1 for numerical stability at very small rates. It rounds M to the nearest cent.

Zero-interest loans

A $12,000 loan over 24 months at 0% requires $500 per month. An extra $100 per month pays it off in 20 months. A zero financed balance has no loan payments or loan payoff date.

How each payment is allocated

1. Round opening balance × nominal annual interest percentage ÷ 1200 to cents. This is monthly interest.
2. Add the entered extra principal to the scheduled payment.
3. Limit the payment to balance + current interest if that is smaller.
4. Subtract current interest from the payment. Apply the remainder to principal.
5. Carry the remaining balance forward, rounded to cents.

At the final scheduled month, collect the exact remaining balance plus that month’s interest. The last payment can be slightly above or below the normal payment because of rounding. Extra-payment scenarios keep the original scheduled payment fixed and end earlier when possible. Extra payments are assumed timely, penalty-free and applied after current interest.

Dates and interest accrual

The start date is the loan or balance date, not the first payment date. Payment 1 is one calendar month later, plus any student grace months. Each date uses the original day of month, clamped to the last valid day of a shorter month. January 31 therefore becomes February 28 (or 29), then March 31. Dates do not change the modeled interest, which is monthly, not daily. Weekends, holidays, irregular first periods and daily accrual are excluded.

Student grace period

No payments occur during the modeled grace period and grace interest does not compound until capitalization. The visitor chooses: add accrued grace interest to principal, pay it separately at repayment start, or assume no accrual. Capitalized grace interest is included in reported total interest once; subsequent interest on that enlarged balance is also included. Separately paid grace interest appears in total repayment but not in the monthly amortization rows.

This is a scenario model. Actual student loans can use daily accrual and different treatment. It does not determine federal income-driven repayment, forgiveness or capitalization rules.

Fees and additional costs

• Personal: fees can be paid upfront, withheld from proceeds, or financed. Withholding reduces net proceeds without changing the stated balance. Financing increases the balance. Interest + fee is the cost of borrowing. Cash repayment totals avoid counting withheld/financed fees twice.
• Mortgage: home price − down payment + financed closing costs determines the balance. Annual property tax and insurance ÷ 12, monthly HOA and entered PMI are added to principal and interest for the housing estimate. These costs are not loan interest. PMI ends only at the month explicitly entered; 0 retains it through payoff. Recurring housing expenses can continue after payoff.
• Auto: vehicle price + sales tax + fees − down payment − trade value + trade payoff determines the balance. Fees are assumed financed and not separately taxable. Tax is on full vehicle price unless the visitor selects trade-value deduction; its base cannot fall below zero. Negative equity increases the balance. No state-specific tax rules are inferred.

Rounding and precision

Inputs representing money are rounded to cents. The payment formula uses JavaScript double-precision arithmetic. The schedule then uses integer cents; interest is calculated with exact integer ratios and half-up cent rounding. Principal, payments, balances and totals use these rounded cent amounts, avoiding binary floating-point drift at half-cent boundaries. Annual taxes and insurance are divided by 12; the combined recurring housing amount is rounded to cents, so independently rounded display components can differ by one cent from the combined total.

The formula assumes equal monthly periods. Lenders may use daily interest, different rounding rules, payment allocation or fees. Even identical inputs can produce small differences. Do not treat these estimates as a payoff quote.

Independently checked numerical examples

These examples were checked against a separate Python Decimal calculation with 50-digit precision and half-up cent rounding during development. This is a software check, not a financial professional’s review.

The auto example uses full-price tax and the homepage inputs. The mortgage example excludes PMI, HOA and closing costs; taxes and insurance are outside the interest total. The other examples have no fees, grace period or extra payments.

Additional checks

• $10,000 at 6% with 6 grace months accrues $300 using the monthly simple-interest assumption; capitalization produces a $10,300 repayment balance.
• $20,000 personal loan + $500 financed fee produces $20,500 financed; withholding that same fee leaves $19,500 of proceeds and $20,000 financed.
• $30,000 car + $1,875 sales tax + $500 fees − $3,000 down − $5,000 trade + $7,000 old debt produces $31,375 financed.
• $350,000 home − $70,000 down produces $280,000 financed. $4,200 annual tax + $1,800 annual insurance add $500 to the monthly principal-and-interest payment.

Sources and corrections

• CFPB: Interest rate and APR
• CFPB: Removing private mortgage insurance
• CFPB: Trading in a vehicle with an unpaid loan
• CFPB: Simple and precomputed auto loan interest
• Federal Student Aid: Interest rates and fees
• Federal Student Aid: Subsidized and unsubsidized loans
• Federal Student Aid: Capitalized interest
• Federal Student Aid Repayment Calculator

Government sources explain concepts and rules; they do not certify this implementation. To report a discrepancy, email rubiconshop213@gmail.com with the calculator, non-sensitive example inputs, expected result and observed result. Do not send account numbers or private loan documents.