Mortgage Payment Calculator: Principal & Interest 2026

One formula turns a house price into a monthly payment

A $400,000.00 home with 20% down leaves a loan of $320,000.00. At 6.5% APR over 30 years the monthly principal & interest is $2,022.62 — 360 payments of $2,022.62 add up to $728,142.36, of which $408,142.36 is interest and $320,000.00 is the loan itself. The first payment is November 2026 and the last is October 2056. On the defaults — $400,000.00 price, 20% down, 6.5% APR, 30 years, $0.00 extra — the down payment is $80,000.00, the loan is $320,000.00, the monthly payment is $2,022.62, the total paid is $728,142.36 and the total interest is $408,142.36.

Check the identities: loan = home price × (1 − down %); monthly rate = APR ÷ 12; payments = years × 12; payment = L·r(1+r)^n / ((1+r)^n − 1); total paid = payment × payments; total interest = total paid − loan. At the defaults the payment is $2,022.62, the total paid is $728,142.36 and the total interest is $408,142.36. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum.

The worked example, line by line

Setup: $400,000.00 home, 20% down, 6.5% APR, 30 years, $0.00 extra.

Line 1 — the loan amount. $400,000.00 × (1 − 0.20) = $320,000.00. The down payment is $400,000.00 × 0.20 = $80,000.00.

Line 2 — the monthly rate. 6.5% ÷ 12 = 0.5417% a month, or 0.0054167 as a decimal.

Line 3 — the payments. 30 years × 12 = 360 payments.

Line 4 — the formula. M = $320,000.00 × 0.0054167 × (1.0054167)^360 / ((1.0054167)^360 − 1) = $2,022.62 a month.

Line 5 — the totals. $2,022.62 × 360 = $728,142.36 paid in total, minus the $320,000.00 loan = $408,142.36 of interest. The first payment is November 2026 and the last is October 2056.

Reverse: the loan amount for a $2,500/mo payment is $395,527.05 (exact $395,527.0488); the home price at 20% down is $494,408.81; the forward is $2,500.00/mo. The APR for a $2,000/mo payment is 6.39% (exact 6.3923%); at 6.39% the payment is $1,999.52, at the exact 6.3923% it is $2,000.00. The longest whole-year term whose total interest stays under $200,000 is 16 years (interest $195,527.84); at 17 years it is $209,499.86 — total interest falls as the term shortens, so this is the longest term under the cap, not the first term under it. The extra payment to pay the loan off in 20 years is $363.22/mo (exact $363.2164); the 20-year payment is $2,385.83; with the rounded extra the loan ends in 240 months with total interest $252,599.26 and interest saved $155,543.11 — derived from unrounded values; the rounded parts ($408,142.36 − $252,599.26) give $155,543.10, one cent less. The loan amount for a $1,500/mo payment is $237,316.23 (exact $237,316.2293); the home price at 20% down is $296,645.29; the forward is $1,500.00/mo. The down payment % for a $300,000 loan on a $400,000 home is 25.00% (exact 25.0000%).

Every branch, checked

Down 10%: Loan $360,000.00, payment $2,275.44/mo, total interest $459,160.16, total paid $819,160.16, payoff October 2056 (360 payments). Halving the down payment raises the loan to $360,000.00 and the payment to $2,275.44 — and the smaller down payment is usually below 20%, so PMI would be added on top in real life.

APR 7.5%: Loan $320,000.00, payment $2,237.49/mo, total interest $485,495.11, total paid $805,495.11, payoff October 2056 (360 payments). One extra point of rate lifts the payment to $2,237.49 and the total interest to $485,495.11 — $77,352.75 more interest than at 6.5%.

Price $500,000: Loan $400,000.00, payment $2,528.27/mo, total interest $510,177.95, total paid $910,177.95, payoff October 2056 (360 payments). The loan is $400,000.00 and the payment is $2,528.27 — the same payment as a 0% down payment on the $400,000.00 home, because the loan is the same $400,000.00.

15-year term: Loan $320,000.00, payment $2,787.54/mo, total interest $181,757.84, total paid $501,757.84, payoff October 2041 (180 payments). The payment rises to $2,787.54, but the total interest falls to $181,757.84 — saving $226,384.52 against the 30-year loan — and the payoff moves to October 2041.

Extra $200/mo: Loan $320,000.00, payment $2,022.62/mo, total interest $408,142.36, total paid $728,142.36, payoff October 2056 (360 payments); with $200.00 extra: 281 months, interest $302,713.69, saved $105,428.67 (79 months saved), payoff March 2050. The loan ends in 281 months (March 2050), 79 months early, and the total interest falls to $302,713.69 — saving $105,428.67.

Extra $500/mo: Loan $320,000.00, payment $2,022.62/mo, total interest $408,142.36, total paid $728,142.36, payoff October 2056 (360 payments); with $500.00 extra: 216 months, interest $222,589.92, saved $185,552.45 (144 months saved), payoff October 2044. The loan ends in 216 months (October 2044), 144 months early, and the interest saved is $185,552.45.

What the defaults assume

The model assumes principal & interest ONLY — property taxes, homeowner’s insurance, PMI and HOA dues are NOT included, so the real monthly bill is higher. It assumes a fixed rate and equal monthly payments for the whole term, and that the first payment month is the month after closing. It assumes the extra-payment simulation pays the extra toward principal every month, and that the loan is paid off in the month the remaining balance, rounded to cents, reaches $0.00 — a sub-cent residual is a rounding artifact, not a real extra month. At 0% down the loan is $400,000.00 and the payment is $2,528.27. At 0% APR the payment is $888.89 — $320,000.00 ÷ 360, no interest at all. Over 10 years the payment is $3,633.54 and the total interest is $116,024.23. At 100% down the loan is $0.00 and the payment is $0.00 — model-level, there is no loan to pay, and the calculator still returns $0.00 rather than an error. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum; the reverses are nearest-value solutions, and the exact unrounded figures ($395,527.0488, 6.3923%, $363.2164, $237,316.2293) are stated wherever the rounded figures appear.

Output · formula · meaning

Who uses this

• The first-time buyer checking a $400,000 listing: they learn the payment is $2,022.62 a month — and they check the 10% down branch ($2,275.44) to see what a smaller down payment costs.
• The buyer choosing between a 15- and a 30-year loan: they learn the 15-year payment is $2,787.54 but saves $226,384.52 of interest — and they check the extra-$200 branch ($105,428.67 saved) for the middle path.
• The homeowner with $200 a month to spare: they learn it ends the loan in 281 months (March 2050) — and they check the $500 branch (216 months) to see what doubling it does.
• The buyer with a $2,000 monthly budget: they learn the APR has to be 6.39% — and they check the $2,500 reverse ($395,527.05 loan) to see what a bigger budget buys.

Accuracy & limitations

The math is first-principles amortization: payment = L·r(1+r)^n / ((1+r)^n − 1); total paid = payment × n; total interest = total paid − loan; the extra-payment simulation runs month by month and stops when the remaining balance, rounded to cents, reaches $0.00. The 4-decimal exact is shown where the rounding matters: the APR for a $2,000/mo payment is 6.3923% (shown as 6.39%); the extra payment for a 20-year payoff is $363.2164/mo (shown as $363.22/mo). What the model cannot do is price YOUR loan: it is principal & interest only — taxes, insurance, PMI and HOA are not included, the rate is assumed fixed for the whole term, and real lenders round each monthly payment to cents, which shifts the final payment by a few cents. For whether you can afford the home, see the mortgage calculator; for the extra-payment plan in detail, see the mortgage extra payment calculator; for the 15- vs 30-year choice, see the 15-year vs 30-year mortgage comparison; and for renting instead, see rent vs buy. This is a calculator, not financial advice.