Mortgage Payment Calculator

Monthly principal and interest, PMI above 80% LTV, total monthly payment, and the lifetime interest and PMI cost.

A mortgage payment calculator turns a home price, a down payment and an interest rate into the numbers a lender quotes. The loan is homePrice − downPayment, and the monthly principal and interest comes from the annuity formula PMT = loan × r ÷ (1 − (1 + r)^−n), where r = APR ÷ 12 and n = years × 12. PMI is charged only while the loan-to-value ratio stays above 80%: LTV = loan ÷ homePrice, and monthly PMI = (annual PMI rate ÷ 12) × loan. Example: 400,000 with 80,000 down at 6.5% over 30 years gives a 320,000 loan, 2,022.62 a month and 408,142.36 of interest. Putting only 40,000 down lends 360,000 (LTV 90%) and adds 150.00 of PMI a month — 54,000.00 over the full term. With a 0% rate the payment is simply the loan divided by the number of months, so nothing compounds at all.

Formulas:

Loan amount: loan = homePrice − downPayment.
Monthly principal & interest: PMT = loan × r ÷ (1 − (1 + r)⁻ⁿ), where r = APR ÷ 12 and n = years × 12; PMT = loan ÷ n when r = 0.
Loan-to-value: ltv = loan ÷ homePrice.
PMI per month: pmi = (PMI rate ÷ 12) × loan, applied only when the PMI rate is filled in and ltv > 0.80; otherwise 0.
Total monthly payment: totalMonthly = PMT + pmi.
Total interest: totalInterest = PMT × n − loan.
Total PMI: totalPMI = pmi × n.

How a mortgage payment is built

A mortgage payment has two moving parts: the principal you borrowed and the interest charged on the balance that is still outstanding. Everything on this page assumes a fixed-rate, fully amortizing loan — the payment stays the same and nothing is left owing after the last month.

The annuity formula behind the payment

The payment solves PMT = loan × r ÷ (1 − (1 + r)⁻ⁿ), with the monthly rate r = APR ÷ 12 and the number of payments n = years × 12. On a $320,000.00 loan at 6.5% for 30 years the result is $2,022.62. The split inside that payment moves every month: the first instalment is $1,733.33 of interest and only $289.28 of principal, and the last one is almost entirely principal.

Down payment sets the loan size, and the loan size sets LTV

Down payment is subtracted first: 20% down on a $400,000.00 home is $80,000.00, so the loan is $320,000.00. The ratio of loan to price is the loan-to-value, ltv = loan ÷ homePrice, and it is the number lenders price risk on. Here it is exactly 80%, the line above which mortgage insurance usually appears.

PMI above 80% LTV

Private mortgage insurance protects the lender, not the buyer, and it is charged while the loan is more than 80% of the home price. Monthly PMI is (annual PMI rate ÷ 12) × loan: put $40,000.00 down on the same $400,000.00 home and the loan becomes $360,000.00 (LTV 90%), so a 0.5% PMI rate adds $150.00 a month on top of the $2,275.44 of principal and interest.

What the payment leaves out

Property taxes, homeowners insurance, flood insurance, HOA dues, closing costs and lender fees are not part of the result, and neither are the mortgage-insurance schemes other countries use instead of PMI. Escrow those separately. The figure here is the loan payment itself, which is what a lender quotes before escrow and what you compare against a rival offer.

Term and rate: what actually moves the payment

Term. The same $320,000.00 at 6.5% costs $2,022.62 a month over 30 years and $2,787.54 over 15 — $764.93 more every month, but the interest falls from $408,142.36 to $181,757.84, a saving of $226,384.52. Shorter terms trade monthly breathing room for a smaller total.

Rate. A half-point matters more than it sounds. At 6.0% instead of 6.5% the payment drops to $1,918.56 — $104.06 lower — and the lifetime interest drops to $370,682.20, saving $37,460.16. Because the rate multiplies a balance that stays high for years, shopping half a point is worth more than most closing-cost negotiations.

PMI: what it costs and when it stops

PMI is a percentage of the loan, so it scales with the down payment rather than with the home. On the LTV 90% example, 0.5% of $360,000.00 is $150.00 a month, which is about 6% of the $2,425.44 total payment and $54,000.00 over the full 30-year term — a real cost, not a rounding error.

In practice PMI is temporary: it is charged while the balance is above 80% of the original value, and US lenders must cancel it on request once the loan reaches 80% of the original value, with automatic termination at 78%. This calculator keeps charging PMI for the whole term because it does not model that removal date — clear the PMI field to see the payment after it drops, and read the balance curve to judge roughly when that will be.

PMI also is not the same product as mortgage life or disability insurance, which pays off the loan for the borrower's family. Only the PMI rate field above feeds the result; everything else belongs in your own budget.

Reading the balance and interest chart

The chart plots two curves for the whole term: the remaining balance falling from the loan amount to zero, and the interest paid to date climbing to the total interest figure. Their crossing point is the moment the loan turns in your favour — before it, most of each payment is interest; after it, most of the payment attacks the principal. Adding a larger down payment lowers the starting point of the balance curve, while a shorter term steepens it.

The same numbers in Excel and on a TI-84

The payment is a single spreadsheet function, which makes it easy to check this page against your own sheet:

Excel payment: =PMT(0.065/12, 360, -320000) = $2,022.62. The same call on a 15-year term (=PMT(0.065/12, 180, -320000)) gives $2,787.54.
Excel total interest: =2022.62*360-320000 = $408,142.36; at 6.0% the payment is $1,918.56 and the interest $370,682.20.
Excel PMI: =0.005/12*360000 = $150.00 a month, so =150*360 = $54,000.00 over the term; the LTV is =360000/400000 = 0.90.
TI-84 steps:
1. Press 2nd → CLR TVM to reset the TVM registers.
2. Enter N=360, I/Y=0.5416667 (6.5 ÷ 12), PV=−320000, FV=0, then move to PMT and press ALPHA → SOLVE → 2022.62.
3. For the 15-year case change only N=180 and solve again → 2787.54.

Worked examples

Example 1: 400,000 home, 80,000 down, 6.5%, 30 years

LTV is exactly 80%, so no PMI is charged even if a rate is entered. Loan: $320,000.00; monthly principal and interest: $2,022.62; PMI: $0.00; total monthly payment: $2,022.62; total interest: $408,142.36; total PMI: $0.00.

Example 2: the same home with 40,000 down (LTV 90%) and a 0.5% PMI rate

Loan: $360,000.00; monthly principal and interest: $2,275.44; PMI: $150.00; total monthly payment: $2,425.44; total interest: $459,160.16; total PMI: $54,000.00. The smaller down payment costs more three times over: a bigger loan, a higher rate of interest on it, and an insurance premium on top.

Example 3: 300,000 home, 60,000 down, 0% APR, 15 years

With no interest the formula collapses to loan ÷ n. Loan: $240,000.00; monthly payment: $1,333.33; total interest: $0.00; PMI: $0.00. It is the quickest way to confirm the calculator is dividing by 180 payments and not compounding anything.

Related tools

The Mortgage Payment Calculator answers "what will I pay each month?". Related questions:

"What does a generic loan look like?" — the Loan Calculator runs the same equal-payment amortization for any principal, with a month-by-month schedule and an extra-payment column.
"How much sooner could I be debt-free?" — the Early Mortgage Payoff Calculator shows the years and interest saved by paying extra every month or in one lump sum.
"How much can I borrow?" — the Mortgage Affordability Calculator turns an affordable monthly payment into a maximum loan and total home price.
"What if the principal were repaid evenly instead?" — the Fixed-Principal Loan Calculator models equal principal payments, where the monthly amount starts higher and declines.

Frequently asked questions

How is a mortgage payment calculated?

The loan is the home price minus the down payment, and the monthly principal and interest comes from the annuity formula PMT = loan × r ÷ (1 − (1 + r)⁻ⁿ), where r = APR ÷ 12 and n = years × 12. A 400,000 home with 80,000 down at 6.5% over 30 years leaves a 320,000 loan and a 2,022.62 monthly payment; the first payment is 1,733.33 of interest and only 289.28 of principal. Over the 360 payments the interest adds up to 408,142.36 on top of the 320,000 borrowed.

What is PMI and when do I pay it?

PMI (private mortgage insurance) protects the lender when the loan-to-value ratio is above 80%, that is when the loan is more than 80% of the home price. Monthly PMI = (annual PMI rate ÷ 12) × loan. Putting 40,000 down on the same 400,000 home lends 360,000 (LTV 90%) and a 0.5% PMI rate adds 150.00 a month, or 54,000.00 across a 30-year term. In practice PMI is temporary: it is charged while the balance stays above 80% of the original value, and in the US a borrower may ask for cancellation at 80% and gets automatic termination at 78%. This calculator does not model that cancellation date, so the total PMI figure assumes the rate is charged for the full term — a conservative upper bound; to model the payment after PMI ends, clear the PMI field.

Does a bigger down payment lower the monthly payment?

Yes, twice over. A larger down payment shrinks the loan and can push the loan-to-value ratio to 80% or below, which removes PMI altogether. On a 400,000 home at 6.5% for 30 years, 80,000 down gives a 320,000 loan and 2,022.62 of principal and interest with no PMI. Halving the down payment to 40,000 pushes the loan to 360,000, the payment to 2,275.44, and adds 150.00 of PMI, so the total monthly payment becomes 2,425.44.

Is a 15-year mortgage cheaper than a 30-year mortgage?

Cheaper in total interest, more expensive every month. The same 320,000 loan at 6.5% costs 2,787.54 a month over 15 years against 2,022.62 over 30 years — 764.93 more each month — but the lifetime interest falls from 408,142.36 to 181,757.84, a saving of 226,384.52. The shorter term wins if the higher payment fits the budget, because every extra dollar goes to principal rather than to interest.

What is not included in the monthly payment?

This calculator models principal, interest and PMI only. Property taxes, homeowners insurance, flood insurance, HOA or condo dues, closing costs and lender fees are all outside the result, and so are local mortgage-insurance schemes that replace PMI in other countries. Budget those separately; the number here is the loan payment a lender quotes before escrow.

What happens when the interest rate is 0%?

The payment becomes simple division: loan ÷ n, with no interest at all. A 300,000 home with 60,000 down over 15 years borrows 240,000 and repays 1,333.33 a month for 180 months, so the total interest is 0.00 and every dollar of the payment reduces the balance. A 0% APR is rare in a real mortgage but it is the cleanest way to check the calculator against your own arithmetic.