Methodology

The loan amount is the home price minus the down payment. The monthly principal-and-interest payment is M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the loan amount, r is the annual rate divided by 100 and by 12, and n is the term in years times 12. At a 0% rate the payment is simply P ÷ n. The calculator shows no result if the loan amount or the rate is zero or less.

Property tax, homeowners insurance, PMI and HOA fees are entered as flat monthly amounts and added to principal and interest to give the total monthly payment. PMI is not removed at any loan-to-value ratio. For an Arizona home, the Arizona Property Tax Calculator estimates what to enter in the property tax field.

The bi-weekly option sets the payment to half the monthly payment, paid 26 times a year, with interest accruing at the annual rate divided by 26. The monthly equivalent shown is that payment × 26 ÷ 12.

The current payment is the standard payment formula applied to your current balance, current rate and years left. The new payment applies the same formula to the new loan amount at the new rate and term. The new loan amount is your balance, or your balance plus closing costs if you roll them into the loan. Rolling them in means $0 is due at closing.

A loan's cost through a given month is its closing costs plus the interest paid so far, where interest paid is the payments made minus the principal repaid. Each loan's payments stop at its own term, after which its cost stops growing. Break-even is the first month the new loan's cost is at or below the old loan's. The falls-behind month is the first later month the new loan's cost is above the old loan's again. It can happen when the new loan is longer and keeps accruing interest after the old loan is paid off.

Simple payback is closing costs ÷ monthly savings, rounded up. It is shown as a secondary figure, and only when the payment drops and there are closing costs. Net at the years you keep the loan is the old loan's cost minus the new loan's cost at that month, so a positive number means refinancing saves. Because cost counts interest rather than principal, this figure already includes the difference in what you still owe on each loan.

The full-loan total for each loan is its remaining payments, plus the cash due at closing for the new loan. The "Over the full loan" figure is the current loan's total minus the new loan's total. When the new loan is longer, it can be negative even when the monthly payment falls and the hold-period figure is positive.

The base loan is the home price minus the down payment, and the loan-to-value ratio (LTV) is the base loan ÷ home price. The upfront mortgage insurance premium (MIP) is 1.75% of the base loan and is added to the loan, so principal and interest are calculated on the base loan plus the upfront MIP using the standard payment formula.

The annual MIP rate is chosen from the table below using the term, the LTV and whether the base loan (before the upfront MIP) is above $726,200. Monthly MIP is the base loan × the annual rate ÷ 12. It is held constant and is not recalculated as the balance falls. The total monthly payment is principal and interest, plus monthly MIP, plus the monthly property tax and insurance you enter.

You enter the balance you owe now (a new loan amount or an existing balance), the rate, and the years left. The scheduled payment is the standard payment formula applied to that balance over the months left. Each period, interest is the remaining balance × the periodic rate, and the rest of the scheduled payment reduces principal. Monthly schedules use 12 periods a year at the rate ÷ 12. Bi-weekly schedules use 26 periods a year at half the monthly payment and the rate ÷ 26, which equals 13 monthly payments a year. A rate of 0 is not accepted.

Extra payments are applied entirely to principal in the period they are paid. On a monthly schedule, the monthly extra is added to every payment, the yearly extra to every 12th payment counted from today, and the one-time extra to the month you choose. On a bi-weekly schedule the extras keep their real size: the monthly extra × 12 ÷ 26 is added to every period, the yearly extra to every 26th period, and the one-time extra to the period that contains the month you choose. Every principal payment is capped at the remaining balance, and the totals count only what is actually paid. The schedule ends when the balance reaches zero, and a bi-weekly payoff is converted to months as periods × 12 ÷ 26, rounded up.

Interest saved and time saved compare the schedule with extras to the same loan paid monthly with no extras. The target-payoff card finds the smallest extra monthly payment, to the cent, that pays the loan off within the years you enter, by repeatedly testing amounts until the payoff month fits; it assumes monthly payments and no other extras. The schedule is numbered by year and payment, with no calendar dates, and your servicer’s actual payoff figure may differ.

Monthly income is annual income ÷ 12. The front-end limit is 28% of monthly income. The back-end limit is 36% of monthly income minus your monthly debt payments. The maximum monthly housing payment is the lower of the two.

The monthly property tax and insurance you enter are subtracted from that payment to leave the maximum principal-and-interest payment. That payment is converted to a loan amount with the present-value form of the payment formula, L = M × [(1+r)^n − 1] / [r(1+r)^n], using a 30-year term. The maximum home price is that loan amount plus your down payment. If nothing is left after taxes and insurance, no result is shown. PMI and HOA fees are not modeled.

The loan is the home price minus the down payment, on a 30-year fixed schedule using the standard payment formula. For each year you plan to stay, rent cost adds 12 months of rent, and rent then rises by the annual rent-increase percentage. Ownership cost starts at the down payment and each year adds 12 mortgage payments plus the annual property tax and insurance you enter, which stay constant.

The loan balance is reduced month by month along the amortization schedule, and the home value rises by the appreciation percentage each year. Equity is home value minus loan balance. The break-even year is the first year in which equity is greater than total ownership cost minus total rent cost.

The top section compares two loan offers on the same loan amount. For each offer, the monthly payment uses the standard payment formula. Upfront cost is the loan amount × points ÷ 100, plus lender fees. Interest paid over your hold period is the payments made in those months (the hold period or the loan term, whichever is shorter) minus the principal repaid, which is the loan amount minus the remaining balance after those months. Total cost over the hold period is the upfront cost plus that interest.

The comparison shows Offer B minus Offer A for upfront cost and monthly payment. The break-even month is the first month in which the higher-upfront offer’s upfront cost plus interest paid so far is no more than the other offer’s; it is blank if that never happens within the shorter term or the upfront costs are equal. This counts the interest saved by a lower rate, so it is the same basis as the total-cost line, and the verdict follows the total cost at your hold period.

Separately, when one offer costs more upfront and less per month, the payback month is the upfront difference ÷ the monthly difference, rounded up. This counts payment savings only, so for two loans of the same term it is later than the break-even month. The years you expect to keep the loan is your assumption, from 1 to 30. Rates must be above 0.

The lower section uses the home price minus the down payment as the loan. Four scenarios run through the same amortization schedule: a 30-year fixed loan at the 30-year rate, a 15-year fixed loan at the 15-year rate, the 30-year loan with an extra amount added to every monthly payment, and the 30-year loan with one extra monthly payment applied each year. The last row approximates bi-weekly payments, and its payment is the regular monthly amount. Total interest and total paid come from each schedule, and payoff is shown as years and months.

The cost of points is the loan amount × the number of points ÷ 100. The new rate is the base rate minus the number of points × the rate reduction per point. The reduction per point is an input you enter (0.25% is the starting value, and lenders vary), not a lender quote. Both payments use the standard payment formula on the same loan amount and term, with no fees on either loan, and monthly savings is the difference. Points are limited to 5, the reduction per point to 1%, and the base rate to 25%. The years you keep the loan are whole years from 1 to the loan term.

The headline break-even month compares the loan with no points to the loan with points, the same way the Mortgage Comparison Calculator does. It is the first month in which the cost of the points plus the interest paid through that month is no more than the interest paid through that month without points. Interest paid is the payments made minus the principal repaid. This counts the interest the lower rate saves, because the lower rate also pays principal down faster. If that never happens within the loan term, the page says the points do not pay for themselves.

The simple payback month is shown beside it as a second figure: the cost of points ÷ monthly savings, rounded up. It counts payment savings only, so it is later than the break-even month. Net savings at your planned holding period is monthly savings × months held, plus the difference between the two loans’ remaining balances at that month, minus the cost of points. It has the same sign as the break-even test, and the sentence above the results is built from it. Net savings over the full term is monthly savings × total months minus the cost of points. The cost table repeats the calculation for 1, 2 and 3 points with your other inputs.

A county’s effective rate is the U.S. Census Bureau American Community Survey median real estate taxes paid ÷ the median home value, for owner-occupied homes. The estimate for a home price is the price × that rate, and the monthly amount is the annual figure ÷ 12. Each county uses the 2025 one-year release where the Census publishes one, and the 2020–2024 five-year release otherwise. The release is shown beside each county.

The figures are fetched from the Census Bureau at each site build. If the fetch fails or no key is set, the build keeps a dated snapshot stored in the site, and the retrieval date on the page is the snapshot’s date. Because the figures are what owners actually paid, the county estimates already reflect credits such as the homeowner rebate. A county is marked as a small sample when the margin of error on its median tax is more than 10% of the estimate.

The optional Arizona method uses the tax-bill formula: Limited Property Value × 10% gives the assessed value, and the annual tax is the assessed value × the combined rate per $100 ÷ 100. The monthly amount is the annual figure ÷ 12. You enter the value and the rate from your own notice of value and tax bill. This result is before credits, so it can run higher than your bill. The rules come from the Arizona Department of Revenue, “Arizona Property Taxation” (February 2024).