What will my mortgage payment be?

How it works

Write V for the home price, D for the down payment, r for the rate ÷ 12 (as a decimal), and n for the months (years × 12). The base loan is B = V − D, which must be more than 0, and the loan-to-value (LTV) is B × 100 ÷ V.

1. Loan amount and upfront fee.

• Conventional: no upfront fee; the loan is L = B.
• FHA: the down payment must be at least 3.5% of the price (LTV at most 96.5%). The upfront premium is 1.75% of B and is added to the loan: L = B × 1.0175.
• VA: the funding fee is a percent of B from the VA's table, added to the loan: L = B + fee. First use: 2.15% with less than 5% down, 1.5% from 5%, 1.25% from 10%. Used before: 3.3%, 1.5%, 1.25%. Exempt: 0.

2. Principal and interest. P = L × r ÷ (1 − (1 + r)^−n), or L ÷ n at 0%.

3. Mortgage insurance for payment number k (1, 2, 3, …), where "balance before" is the balance before that payment:

• Conventional with LTV above 80%: PMI = the PMI rate × B ÷ 12, charged while the balance before is above 78% of V and k is at most n ÷ 2 (the midpoint). With LTV of 80% or less there is no PMI.

• FHA: HUD's annual premium rate a (in basis points ÷ 10,000) comes from Mortgagee Letter 2023-05, by term, base loan, and LTV:

  • Term over 15 years, base loan up to $726,200: LTV up to 90%, 0.50% for 11 years; over 90% up to 95%, 0.50% for the whole term; over 95%, 0.55% for the whole term.
  • Term over 15 years, base loan over $726,200: LTV up to 90%, 0.70% for 11 years; over 90% up to 95%, 0.70% for the whole term; over 95%, 0.75% for the whole term.
  • Term of 15 years or less, base loan up to $726,200: LTV up to 90%, 0.15% for 11 years; over 90%, 0.40% for the whole term.
  • Term of 15 years or less, base loan over $726,200: LTV up to 78%, 0.15% for 11 years; over 78% up to 90%, 0.40% for 11 years; over 90%, 0.65% for the whole term.

  Following HUD's calculation method, for each loan year y the premium is a × (the average of the 12 scheduled balances at the start of months 12(y − 1) + 1 to 12y), paid in 12 equal monthly parts. The scheduled balances are those of the base loan B on its original schedule: after j payments, B(1 + r)^j − p((1 + r)^j − 1) ÷ r, with p = B × r ÷ (1 − (1 + r)^−n). (HUD averages the balances of the whole loan and divides by 1 + the upfront factor, which gives the same number.) The premium is charged for payments 1 to 132 when paid for 11 years, or for every payment otherwise.

• VA: none.

4. Other monthly costs. Property tax = the yearly tax rate × V ÷ 12. Home insurance = the yearly premium ÷ 12 (a monthly amount is used as typed). HOA dues are monthly (a yearly amount is divided by 12).

5. Monthly payment (the headline) = P + the first month's mortgage insurance + property tax + home insurance + HOA dues.

6. Schedule. For each month: interest = balance × r; if this is payment n, or P + extra − interest is at least the balance, the payment clears the balance; otherwise principal = P + extra − interest. Each row adds that month's mortgage insurance, tax, insurance, and HOA dues. Totals: interest, mortgage insurance, and the number of months with mortgage insurance are summed over the rows; the total cost is D plus everything paid in every row. With an extra amount, interest saved is n × P − L minus the interest with the extra, and months saved is n minus the number of payments.

Assumptions

• The rate is fixed, and the first payment is one month after the start date.
• The home's original value for PMI is the price. PMI stops once the balance falls to 78% of it; without extra payments that is the date the Homeowners Protection Act sets for automatic termination. You can also ask for cancellation at 80%, which this page does not assume.
• FHA premiums and VA fees are those in effect for loans from March 20, 2023 (FHA) and April 7, 2023 (VA); FHA and conforming loan limits by county are not checked.
• Property tax, insurance, and HOA dues stay the same for the whole loan. Closing costs are not included.
• Values are not rounded to the cent between months; HUD rounds the FHA premium to the cent.

Worked examples by hand

A $400,000 home, 20% down, 6.5% over 30 years, 1.1% property tax, $1,800 a year of insurance. L = 320,000, r = 0.065 ÷ 12 = 0.0054167, and (1 + r)^−360 = 0.143025, so P = 320,000 × 0.0054167 ÷ 0.856975 = $2,022.62. Tax is 0.011 × 400,000 ÷ 12 = $366.67 and insurance 1,800 ÷ 12 = $150. With 20% down there is no PMI, so the monthly payment is $2,539.28. The interest over 30 years is $408,142.36.

A $300,000 home, 10% down, 7% over 30 years, PMI 0.5% a year. L = 270,000 (LTV 90%), P = $1,796.32, and PMI = 0.005 × 270,000 ÷ 12 = $112.50 a month. PMI stops once the balance is no longer above 0.78 × 300,000 = $234,000: the balance before payment 115 is $234,308.42 and before payment 116 it is $233,878.90, so PMI is paid 115 months, $12,937.50 in all.

An FHA loan: a $300,000 home, 3.5% down, 6.25% over 30 years. B = 289,500 and LTV = 96.5%, so the upfront premium is 0.0175 × 289,500 = $5,066.25 and L = $294,566.25. With r = 0.0625 ÷ 12 and (1 + r)^−360 = 0.154103, P = 294,566.25 × 0.0052083 ÷ 0.845897 = $1,813.70. The LTV is over 95% on a 30-year loan with a base loan under $726,200, so the annual premium is 0.55% for the whole term (360 months). The base loan's payment is $1,782.50, and its first 12 scheduled balances average $287,962.67, so the first year's monthly premium is 0.0055 × 287,962.67 ÷ 12 = $131.98.

The first loan with $300 extra each month (no tax or insurance). Each month pays $2,322.62 against the balance. Running the monthly rule, the loan ends after 254 payments, 106 months sooner, with $269,696.46 of interest. Without the extra the interest is 360 × 2,022.618 − 320,000 = $408,142.36, so the extra saves $138,445.90.

A VA loan: a $350,000 home, no down payment, first use, 6% over 30 years. The funding fee is 2.15% × 350,000 = $7,525, so L = $357,525. (1.005)^−360 = 0.166042, so P = 357,525 × 0.005 ÷ 0.833958 = $2,143.54, with no monthly mortgage insurance ($0).