How Money Anvil calculates

Every number on this site comes from a formula on this page. Last reviewed October 13, 2026.

Monthly payment

A fixed-rate loan's principal-and-interest payment is the standard annuity formula:

M = P × r ÷ (1 − (1 + r)−n)

where P is the amount borrowed, r the annual interest rate divided by 12, and n the number of monthly payments. At a 0% rate the payment is simply P ÷ n. The result is rounded to the nearest cent.

Amortization schedule and rounding

Each month, interest is the remaining balance times r, rounded to the cent, the way lenders do it. The rest of the payment reduces the balance, followed by any extra payment you've entered. Because of that monthly rounding, the very last payment is adjusted by a few cents (occasionally a dollar or so on long loans) so the balance ends at exactly zero. All amounts are kept in whole cents internally, so the schedule's rows always add up to the totals shown.

Taxes, insurance, HOA and PMI

• Property tax is the rate you enter times the home price, divided by 12.
• Home insurance is your yearly premium divided by 12.
• HOA dues are added as entered.
• PMI (private mortgage insurance) applies when the down payment is under 20%: the yearly rate you enter times the loan amount, divided by 12. It's charged until the loan is scheduled to reach 78% of the home's original value, when the Homeowners Protection Act requires it to end automatically. That date follows the original schedule, so extra payments don't move it, though you can usually ask your lender to remove PMI once you reach 80%.

Extra payments

Extra payments go straight to principal after that month's regular payment, and are capped so you never pay more than you owe. "Interest saved" and "time saved" compare the schedule with your extra payments against the same loan without them.

Home affordability

The affordability calculator applies the two debt-to-income limits lenders use, on gross (before-tax) monthly income:

• Housing limit (front-end ratio, 28% by default): income × ratio.
• Total debt limit (back-end ratio, 36% by default): income × ratio, minus your other monthly debt payments.

The lower of the two is the most the full monthly housing payment may be. That payment is worked out exactly as in the mortgage calculator: principal and interest on the price less your down payment, plus tax, insurance, PMI (under 20% down) and HOA. Because it only ever rises with the price, the calculator searches whole-dollar prices by repeated halving and reports the highest one whose payment is at or under the limit.

Refinancing

The current loan's payment is the standard payment on your balance, rate and remaining months (years left × 12, rounded). The new loan is your balance, plus closing costs if you choose to add them to the loan, at the new rate and term. Both are amortized month by month as above.

• Monthly savings is the current payment minus the new one.
• Break-even is the number of payments whose savings cover closing costs paid in cash: costs ÷ monthly savings, rounded up. With costs added to the loan there is nothing to recover up front; their cost appears in the totals instead.
• Total to pay is every remaining payment on the current loan, against every payment on the new loan plus any cash closing costs. Their difference shows whether refinancing saves money over the life of the loan.

Comparisons ignore the time value of money and any investment of the monthly savings, and assume you keep the new loan to the end.

Auto loans

The amount financed is the price plus sales tax and fees, minus the down payment and trade-in value, plus anything still owed on the trade-in. Sales tax is the rate times the taxable price, rounded to the cent; the taxable price is the price minus the trade-in by default (most states), or the full price if you choose. Fees are financed and not taxed. "Total cost of the car" is the price, sales tax, fees and all interest.

Personal loans and APR

An origination fee is the fee rate times the loan amount, rounded to the cent, and is taken out of what you receive. The APR is 12 × the monthly rate i that solves

received = Σk=1…n paymentk ÷ (1 + i)k

using the actual payments, including the slightly different last one. This is the actuarial method of the Truth in Lending Act (Regulation Z). The equation is solved by repeated halving to far beyond the two decimals shown. With no fee, the APR equals the interest rate.

Student loans

For unsubsidized loans, interest before repayment is simple interest: the amount borrowed × the rate ÷ 12, rounded to the cent, for each month until repayment. Servicers accrue it daily, so real figures differ by a few cents. If you let it build up, it is capitalized (added to the balance) when repayment starts; if you pay it, it's counted in the total paid. Subsidized loans accrue nothing before repayment. Repayment is a level-payment schedule over the term you choose.

Interest rates

The default rate is the latest weekly national average for a 30-year fixed mortgage from Freddie Mac's Primary Mortgage Market Survey, published through FRED (Federal Reserve Bank of St. Louis). It's updated when the site is rebuilt, never fetched by your browser. Averages are a starting point; your own rate depends on your credit, down payment, loan type and points.

The auto and personal loan calculators start from the Federal Reserve's average rates at commercial banks on 48-month new car loans and 24-month personal loans (G.19 Consumer Credit, via FRED), published quarterly. Student loan rates are set by law each year, so that calculator starts from an example rate you should replace with your own.

Data sources

• Freddie Mac, 30-Year Fixed Rate Mortgage Average in the United States [MORTGAGE30US] and 15-Year Fixed Rate Mortgage Average in the United States [MORTGAGE15US], retrieved from FRED, Federal Reserve Bank of St. Louis: FRED series page.
• Board of Governors of the Federal Reserve System (US), Finance Rate on Consumer Installment Loans at Commercial Banks, New Autos 48 Month Loan [TERMCBAUTO48NS] and Finance Rate on Personal Loans at Commercial Banks, 24 Month Loan [TERMCBPER24NS], retrieved from FRED, Federal Reserve Bank of St. Louis: FRED series page.

Money Anvil isn't affiliated with or endorsed by Freddie Mac, the Federal Reserve or the Federal Reserve Bank of St. Louis.

What these calculators don't include

• Closing costs, points and lender fees when buying (the refinance calculator takes them as an input).
• Changes in taxes, insurance or HOA dues over time.
• Adjustable-rate loans (all calculators assume a fixed rate).

The results are estimates for planning, not financial advice or an offer of credit; see the terms of use. For a binding figure, use the Loan Estimate your lender gives you.