How we calculate

Every calculator on the site uses one calculation engine. This page explains what it does, how it rounds, and where each program rule comes from, so you can check any number yourself.

The payment and the schedule

A fixed-rate loan is repaid in equal payments. The payment is:

M = P × r ÷ (1 − (1 + r)−n)

where P is the amount borrowed, r the interest rate per payment (the yearly rate ÷ 12 for monthly payments) and n the number of payments. At a 0% rate it's simply P ÷ n. Each payment first pays the interest owed on the balance for that period, and the rest reduces the balance.

Rounding: whole cents, like a lender

The schedule is worked in whole cents. The payment is rounded to the cent, each period's interest is rounded to the cent, and the final payment takes whatever is left so the balance lands on exactly $0.00. Every column of the schedule therefore adds up exactly to its total. Many calculators keep fractions of a cent and only round for display, so their columns don't quite match their totals.

Extra payments

Extra principal, whether every payment or on one chosen payment, is taken off the balance straight away, so it stops costing interest from the next period. The required payment stays the same and the loan ends sooner. The savings shown compare the same loan paid exactly as scheduled. The payoff calculator finds the smallest extra amount, to the cent, that pays the loan off by the date you pick. It searches the same schedule rather than using an approximate formula, so the answer is exact even with one-time extras in the mix.

Payment frequency

• Monthly: 12 payments a year, interest at the yearly rate ÷ 12.
• Twice a month: 24 payments a year, interest at the yearly rate ÷ 24. It's the same loan split in two, so it ends on the same date and saves only a little interest.
• Biweekly: half the monthly payment every two weeks, 26 times a year, with interest at the yearly rate ÷ 26. That's 13 monthly payments' worth a year, which is why it pays off years early. It's available for fixed-rate loans, whose payment doesn't change.

Adjustable rates (ARMs)

The rate stays at its starting level for the fixed period, then moves at each adjustment toward the rate you expect (or as far up or down as the caps allow, for the worst and best cases). The first adjustment is limited by the initial cap, later ones by the periodic cap, and the rate never goes above the starting rate plus the lifetime cap or below the floor. Whenever the rate changes, the payment is recalculated on the balance actually owed, over the time left, as lenders do. The ARM presets use Fannie Mae's standard caps for SOFR ARMs: 2/1/5 for a 5/6 ARM, and 5/1/5 for 7/6 and 10/6 ARMs.

Interest-only and balloon loans

An interest-only loan charges just the interest for its interest-only period, then repays the whole balance over the years left, which is why its payment jumps. A balloon loan's payment is figured over the full term, and whatever is still owed at the balloon date is due in one lump sum.

PMI on conventional loans

With less than 20% down, private mortgage insurance is charged at the yearly rate you enter, on the original loan amount. It ends following the federal Homeowners Protection Act:

• automatically once the balance is scheduled to reach 78% of the home's original value, by the original schedule, whatever you've actually paid;
• in any case at the midpoint of the loan's term;
• or, if you choose the option to ask for it, once the actual balance reaches 80%. Extra payments get there sooner.

FHA, VA and USDA fees

• FHA: an upfront mortgage insurance premium of 1.75% of the base loan, and an annual premium from HUD's table by term, loan size and down payment, currently 0.15% to 0.75% a year. The annual premium is charged on the average scheduled balance of each loan year, and lasts 11 years with at least 10% down, or the life of the loan with less. Source: HUD Mortgagee Letter 2023-05 and Handbook 4000.1.
• VA: a one-time funding fee by down payment and whether it's your first VA loan (for example, 2.15% for a first use with less than 5% down), waived for veterans who are exempt, such as those receiving VA disability compensation. There's no monthly mortgage insurance. Source: VA Circular 26-23-06.
• USDA: an upfront guarantee fee of 1% and an annual fee of 0.35% on the average scheduled balance, for the life of the loan. When the upfront fee is financed it's figured on the total loan, as USDA requires. Source: USDA Rural Development fiscal year 2026 rates.

These figures change by policy letter and fiscal year. They're kept in one dated place in the code and checked against the official sources; the date is shown on each program's calculator.

Affordability

The affordability calculator finds the highest price whose full monthly housing cost fits both limits you set: housing as a share of gross income (front-end ratio), and housing plus other debts (back-end ratio). The housing cost is the loan's actual first payment from the same schedule, including property tax, insurance, PMI or FHA insurance and HOA dues. The price is also limited by the program's minimum down payment: 3% for conventional loans and 3.5% for FHA. The answer is found by a search, to the dollar.

Refinancing

The refinance calculator compares keeping your loan with replacing it by each loan's position every month: everything paid so far plus what's still owed, plus closing costs paid in cash and minus any cash taken out. It breaks even the first month the refinance's position is lower. Unlike the common shortcut (costs ÷ monthly saving), this counts how fast each loan pays down principal. It also shows when a longer new term makes the refinance fall behind for good. The comparison covers principal and interest, since tax and insurance don't change with a refinance.

What the results leave out

Real loans also have lender fees, prepaid interest, escrow cushions and exact payment dates, and each lender has its own rounding and cutoff rules. The results are close estimates for planning, not a loan estimate or an offer. Your lender's Loan Estimate and Closing Disclosure are the official figures for your loan.

Tested

The engine has an automated test suite that runs before every release. It checks, for example, that every schedule pays off exactly what was borrowed, that the FHA table matches HUD's, and that PMI ends when the law says it must. Spotted something that looks wrong? Tell us.