How Mortgage Payments Are Calculated
A transparent, step-by-step breakdown of the standard amortization formula lenders use to compute fixed-rate monthly mortgage payments.
Direct Answer: The Mortgage Payment Formula
A fixed-rate monthly mortgage payment (Principal & Interest) is calculated with the annuity amortization formula:
Where P is the principal borrowed (Purchase Price minus Down Payment), r is the monthly periodic interest rate (Annual Interest Rate ÷ 100 ÷ 12), and n is the total number of monthly payments (Years × 12).
Amortization Formula
The standard banking equation used to establish level monthly mortgage installments.
Monthly Rate & Term
How annual rates convert to monthly interest factors (r = Rate ÷ 100 ÷ 12) across loan terms.
Step-by-Step Math
Clear numerical walkthrough demonstrating how every dollar of your mortgage payment is derived.
Step-by-Step Breakdown of the Formula
1. Calculate the Loan Principal (P)
Your loan principal is not the full home price unless you make a 0% down payment. It is equal to the agreed purchase price minus your upfront down payment cash:
Principal (P) = Home Purchase Price − Down Payment
2. Convert Annual Rate to Monthly Periodic Rate (r)
Mortgage interest is compounded monthly. You must convert your annual nominal percentage into a decimal monthly rate by dividing by 100, then by 12:
r = (Annual Rate in %) ÷ 100 ÷ 12
For example, an annual rate of 6.0% yields a monthly periodic rate of 0.06 ÷ 12 = 0.005.
3. Compute the Total Number of Payments (n)
Multiply the loan term in years by 12 monthly installments:
n = Term in Years × 12
A 30-year loan has n = 360 payments; a 15-year loan has n = 180 payments.
4. Solve for the Monthly Level Payment (M)
Substitute P, r, and n into the amortization equation. The resulting figure (M) is the exact level monthly installment required to fully amortize the loan down to a balance of $0 at the end of period n.
Complete Worked Example: $400,000 Home
Let's calculate the monthly payment for a home buyer purchasing a $400,000 property with 20% down payment and a 30-year fixed loan at 6.0% annual interest:
• Down Payment: $400,000 × 0.20 = $80,000
• Principal (P): $400,000 − $80,000 = $320,000
• Monthly rate (r): 6% ÷ 12 = 0.005
• Number of payments (n): 30 × 12 = 360
• Growth factor (1 + r)^n: (1.005)^360 ≈ 6.022575
• Numerator: 320,000 × 0.005 × 6.022575 ≈ 9,636.12
• Denominator: 6.022575 − 1 = 5.022575
• Monthly Payment (M): 9,636.12 ÷ 5.022575 = $1,918.56
Over 360 monthly payments, total repayment equals $1,918.56 × 360 = $690,682.20, consisting of $320,000 principal and $370,682.20 in cumulative interest.
Assumptions & Limitations
- Nominal Rate vs APR: This formula models nominal interest repayment. It does not calculate the Annual Percentage Rate (APR), which incorporates lender fees, points, and closing costs.
- Excludes Escrow Items: Property taxes, homeowners insurance premiums, and HOA fees are not included in this formula; they must be budgeted separately or added to the monthly payment.
- Fixed-Rate Assumption: The formula assumes an unchanging fixed rate. Adjustable-rate mortgages (ARMs) reset periodic rates according to benchmark indices.
Estimate Your Monthly Mortgage Payment
Use Formulexa's free Mortgage Calculator to test different down payment sizes, explore custom interest rates, and see complete monthly and yearly amortization schedules.