Methodology & Data Sources

Core Principles

1. Client-side only. All calculations run in your browser. No financial data is ever sent to a server, logged, or stored. See Privacy Policy.
2. Standard formulas. Every formula is the industry-standard version used by US lenders, documented in the Truth in Lending Act (Regulation Z) and CFPB guidance.
3. Primary-source data. Rate benchmarks, tax brackets, and thresholds come directly from Federal Reserve, CFPB, IRS, and Freddie Mac — never from third-party aggregators.
4. Estimates, not advice. Results are planning estimates. Your actual numbers may vary based on fees, state taxes, lender-specific terms, and individual circumstances.

Amortization Formula

Fixed-Rate Mortgage / Loan Payment

M = P × [r(1+r)n] / [(1+r)n − 1]

M

Monthly payment (principal + interest)

P

Principal — the loan amount borrowed

r

Monthly interest rate = annual rate ÷ 12 (as a decimal)

n

Total number of payments = loan term in years × 12

In plain language: Your monthly payment is calculated so that after making the same payment every month for the full term, the balance reaches exactly zero. Early payments are mostly interest (because the balance is large). Later payments are mostly principal (because the balance is small). This is why a 30-year mortgage at 6.5% pays more in interest than the original loan amount.

Extra Payment Acceleration

When you add extra principal payments, we recalculate the amortization schedule month by month:

For each month: Interest = remaining_balance × r
             Principal_portion = M − interest + extra_payment
             New_balance = remaining_balance − principal_portion
             Repeat until balance ≤ 0

Every dollar of extra principal eliminates all future interest that dollar would have accrued — this is why small extra payments early in the term have an outsized effect.

Compound Interest

Future Value with Regular Contributions

FV = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]

FV

Future value — total amount at the end

P

Principal — initial lump sum invested

r

Annual interest rate (as decimal, e.g., 0.07 for 7%)

n

Compounding periods per year (12 = monthly, 1 = annually, 365 = daily)

t

Time in years

PMT

Regular contribution per period

In plain language: Your money earns interest, and then that interest earns interest on itself. The first part of the formula grows your initial lump sum. The second part grows your recurring contributions. Both compound. The earlier you start, the more periods of compounding work in your favor — this is why time in the market beats timing the market.

The Rule of 72

A quick mental shortcut for doubling time:

Years to double = 72 ÷ annual_rate_percentage

At 7% return, money doubles in ~10.3 years. At 10%, ~7.2 years. This is an approximation (accurate for rates between 4% and 15%) but useful for quick mental math.

Debt Payoff Orderings

We model two strategies for paying off multiple debts. Both use the same amortization engine — the difference is which debt gets the extra payment first.

Debt Avalanche (Mathematically Optimal)

1. List all debts by APR (highest first)
2. Pay minimums on every debt
3. Direct every extra dollar to the highest-APR debt until it is gone
4. Roll that payment to the next highest-APR debt
5. Repeat until all debts cleared

Minimizes total interest paid. Always the cheapest route mathematically.

Debt Snowball (Behavioral)

1. List all debts by balance (smallest first)
2. Pay minimums on every debt
3. Direct every extra dollar to the smallest-balance debt until it is gone
4. Roll that payment to the next smallest debt
5. Repeat until all debts cleared

May cost more in interest, but the quick wins (clearing small debts fast) improve follow-through. Research from Northwestern's Kellogg School (2023) found snowball users were more likely to become debt-free overall.

Debt-to-Income Ratio (DTI)

Front-End and Back-End DTI

Front-end DTI = (Total Monthly Housing Costs ÷ Gross Monthly Income) × 100
Back-end DTI = (Total Monthly Debt Payments ÷ Gross Monthly Income) × 100

Housing costs

Mortgage P&I + property taxes + insurance + HOA (PITI)

All debt payments

PITI + car loans + student loans + credit card minimums + child support/alimony

Excluded

Utilities, groceries, insurance (non-housing), subscriptions, taxes withheld

In plain language: Lenders use two DTI thresholds. Front-end (housing only) should typically be ≤28%. Back-end (all debt) should typically be ≤36% for conventional loans, ≤43% for FHA. Above 43%, most conventional approval paths close. These thresholds come from the CFPB's Qualified Mortgage rules and Fannie Mae/Freddie Mac guidelines.

28/36 Rule Thresholds

Assumptions & Limitations

• Fixed rates only. We model fixed-rate loans. Adjustable-rate mortgages (ARMs), variable credit card rates, and HELOCs require different modeling — use the results as a baseline.
• Monthly compounding. All calculations assume monthly compounding. Some lenders use daily compounding, which causes minor rounding differences (typically a few cents to a few dollars).
• US focus. Tax brackets, deduction thresholds, and DTI standards are US-specific. The underlying math (amortization, compounding) is universal.
• Results are estimates. Your actual numbers may vary based on lender-specific fees, state/local taxes, PMI, points, and individual credit profile. Always request official quotes before making decisions.
• Not financial advice. PayoffCalcs provides planning tools, not personalized financial advice. For major decisions, consult a licensed professional.

Primary Data Sources

Every data point, rate benchmark, and threshold on this site is traceable to a primary source:

Rate benchmarks and tax data are refreshed on the schedule documented on our Sources page. Last full review: August 2026.

Update Schedule