Your monthly mortgage payment for principal and interest is M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. For example, a $300,000 loan at 6.5% annual interest over 30 years costs $1,896.20 per month in principal and interest. This guide explains each part of the formula, works through that example step by step, explains amortization, taxes, insurance and PMI, and compares 15-year and 30-year loans with verified totals.
If you want the answer for your own numbers without doing the arithmetic, use the free mortgage calculator — enter the loan amount, rate and term and it computes your monthly payment instantly.
What Is the Mortgage Payment Formula?
A fixed-rate mortgage is an amortizing loan: you pay the same amount every month, and each payment covers that month’s interest plus a slice of the principal. The formula finds the fixed monthly payment that exactly pays off the loan, with interest, over the term.
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
- P — principal: the amount you borrow. On a $375,000 home with 20% down ($75,000), P is $300,000.
- r — monthly interest rate: the annual rate divided by 12. At 6.5% annual, r = 0.065 ÷ 12 = 0.0054167.
- n — number of payments: years × 12. A 30-year loan has n = 360 payments; a 15-year loan has n = 180.
- M — monthly payment: principal and interest only. Taxes, insurance, HOA dues and PMI are added on top (see below).
The formula looks intimidating, but each piece is simple: (1 + r)^n is just the compounding factor over the whole loan, and the formula balances it so the loan reaches exactly zero at the final payment.
How Do You Calculate a Mortgage Payment? Step-by-Step
Worked example: $300,000 at 6.5% over 30 years.
- Monthly rate: r = 0.065 ÷ 12 = 0.0054167.
- Number of payments: n = 30 × 12 = 360.
- Compounding factor: (1 + 0.0054167)^360 = 6.9918.
- Numerator: P × r × factor = 300,000 × 0.0054167 × 6.9918 = 11,364.60 (approximately, before rounding).
- Denominator: factor − 1 = 6.9918 − 1 = 5.9918.
- Divide: 11,364.60 ÷ 5.9918 = $1,896.20 per month in principal and interest.
Over 360 payments that totals 360 × $1,896.20 = $682,633.47, of which $382,633.47 is interest — more than the amount borrowed. That is normal for a 30-year loan at this rate, and it is why the term you choose matters so much (see the comparison below).
Second example: $250,000 at 7.0% over 30 years. Here r = 0.07 ÷ 12 = 0.0058333 and n = 360, which gives $1,663.26 per month in principal and interest, or $598,773.60 over the life of the loan. Even a half-point rate difference moves the payment by hundreds of dollars a month on a typical loan, which is why rate shopping matters.
What Does Your Monthly Payment Include?
The formula above covers principal and interest (P&I) only. Most homeowners pay a larger monthly amount that also includes:
- Property taxes (T): set by your local authority, often 0.5%–2% of the home’s value per year, collected monthly into escrow.
- Homeowners insurance (I): required by the lender, covering damage to the property.
- Private mortgage insurance (PMI): usually required when your down payment is under 20%. It protects the lender, not you, and typically costs 0.5%–1% of the loan per year until you reach 20% equity — at which point you can usually ask to have it removed.
- HOA dues: if the property is in a homeowners association, these are billed separately or added to the payment.
Lenders call the full bundle PITI (principal, interest, taxes, insurance). When you compare quotes, always check whether a figure is P&I only or full PITI — mixing them up is the most common budgeting mistake first-time buyers make.
How Does Amortization Work?
Amortization is the schedule by which your fixed payment is split between interest and principal over time. Because interest is charged on the remaining balance, early payments are mostly interest and later payments are mostly principal — even though the total payment never changes.
On the $300,000, 6.5% example, the first payment breaks down like this: interest = $300,000 × 0.0054167 = $1,625.00, so principal = $1,896.20 − $1,625.00 = $271.20. After that payment the balance is $299,728.80. After 12 payments the balance is about $296,646.87 — you paid $22,754.40 in the first year but only about $3,353.13 of it went to principal. That slow start surprises many buyers, but it is exactly how amortizing loans work: the balance falls slowly at first, then faster every year as the interest portion shrinks.
Extra payments attack the principal directly, which is why even one extra payment a year shortens a 30-year loan by years and saves tens of thousands in interest.
Is a 15-Year or 30-Year Mortgage Better?
There is no universal answer — it is a trade-off between monthly cash flow and total cost. Using the same $300,000 loan at 6.5%:
| 30-year | 15-year | |
|---|---|---|
| Monthly payment (P&I) | $1,896.20 | $2,613.32 |
| Number of payments | 360 | 180 |
| Total paid | $682,633.47 | $470,397.98 |
| Total interest | $382,633.47 | $170,397.98 |
The 15-year loan costs $717.12 more per month but saves $212,235.49 in interest and frees you from the payment 15 years sooner. The 30-year loan costs far more overall but keeps the monthly payment lower and leaves more cash free each month for investing, emergencies, or other goals. A common middle path is a 30-year loan with voluntary extra principal payments — you keep the lower required payment but can still pay it off early when cash allows.
How Does a Down Payment Change Your Payment?
Your down payment reduces P, and the payment falls in proportion. Take the same 6.5%, 30-year terms: borrowing $300,000 costs $1,896.20 per month, while borrowing $240,000 (as on a $300,000 home with 20% down) costs $1,516.96 per month — exactly 20% less, saving $379.24 every month. A bigger down payment also helps you avoid PMI, which is a second saving on top of the lower payment.
One more distinction worth knowing before you shop: everything above assumes a fixed-rate loan, where the rate — and therefore the P&I payment — never changes. An adjustable-rate mortgage (ARM) starts lower but resets with the market after an initial fixed period, so its payment can rise. ARMs can make sense if you plan to move or refinance before the reset, but for most buyers the predictability of a fixed rate is worth the slightly higher starting payment.
That is the full picture for a fixed-rate loan: the formula sets the P&I payment, PITI and PMI set the real monthly bill, amortization explains where each payment goes, and the term sets the total cost. Run your own figures through the free mortgage calculator before you talk to a lender, so you know what payment you can actually afford.
Frequently Asked Questions
What is the formula for calculating a mortgage payment?
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. It gives the fixed monthly principal-and-interest payment for a fixed-rate loan.
How much is a $300,000 mortgage at 6.5% for 30 years?
$1,896.20 per month in principal and interest. With r = 0.065 ÷ 12 = 0.0054167 and n = 360, the compounding factor (1 + r)^n is 6.9918, giving 300,000 × 0.0054167 × 6.9918 ÷ 5.9918 = $1,896.20. Total paid over 30 years is $682,633.47, of which $382,633.47 is interest.
What is included in a monthly mortgage payment?
The formula covers principal and interest only. Most homeowners also pay property taxes and homeowners insurance through escrow (together called PITI), plus PMI if the down payment was under 20%, and HOA dues where applicable. Always check whether a quoted payment is P&I only or full PITI.
Is a 15-year or 30-year mortgage better?
A 15-year loan costs more per month but far less overall: on $300,000 at 6.5%, the 15-year payment is $2,613.32 versus $1,896.20 for 30 years, but total interest is $170,397.98 versus $382,633.47 — a saving of $212,235.49. The 30-year loan keeps monthly cash flow lower; a 30-year loan with extra principal payments is a common middle path.
What is PMI and when does it go away?
Private mortgage insurance protects the lender when your down payment is under 20%, typically costing 0.5%–1% of the loan per year. Once you reach 20% equity in the home you can usually request its removal, and lenders must generally drop it automatically at 22% equity for a primary residence.
Does a bigger down payment lower my monthly payment?
Yes, in direct proportion: it reduces the amount borrowed. At 6.5% over 30 years, borrowing $240,000 instead of $300,000 lowers the payment from $1,896.20 to $1,516.96 per month, saving $379.24 monthly — and a 20% down payment also avoids PMI.
