Fixed-Rate Home Mortgage Payment Calculator
How to Calculate
- Enter Net Loan Principal ($): Input the net loan amount requested after subtracting your cash down payment from the home purchase price.
- Enter Annual Mortgage Rate (%): Input the fixed annual percentage rate quoted by your mortgage lender.
- Specify Loan Term (Years): Choose your repayment horizon (typically 15 or 30 years).
- Review Payment & Interest: The engine generates your exact fixed monthly principal and interest payment alongside lifetime borrowing costs.
Formula Reference
$M = P \left[ \frac{r(1+r)^n}{(1+r)^n - 1} \right]$
The standard fixed-rate amortization equation solves for a uniform monthly payment that fully amortizes principal and interest over the agreed loan term:
- M: Monthly principal and interest payment.
- P: Net borrowed mortgage balance (Home Price − Down Payment).
- r: Periodic monthly interest rate (Annual Interest Rate ÷ 12 ÷ 100).
- n: Total number of monthly installments (e.g., 30 years × 12 = 360 payments).
Practical Example
Worked Mortgage Amortization Example
Calculating the monthly principal and interest payment for a $350,000 loan balance at 6.75% APR over a 30-year (360-month) fixed tenure:
- Periodic Monthly Rate (r): 0.0675 / 12 = 0.005625
- Total Payment Months (n): 30 × 12 = 360 months
- Amortization Compounding Factor: (1 + 0.005625)360 ≈ 7.534725
- Monthly Payment (M):
$350,000 × [0.005625 × 7.534725] / [7.534725 − 1] = $2,269.97 / month - Total Cash Paid Across 30 Years: 360 × $2,269.97 = $817,189.20
- Lifetime Interest Cost: $817,189.20 − $350,000 = $467,189.20
15-Year vs. 30-Year Mortgage Comparison ($350,000 Loan @ 6.75%)
| Term | Monthly Payment | Total Interest Paid | Total Lifetime Outlay | Total Savings |
|---|---|---|---|---|
| 15 Years | $3,097.42 | $207,535.60 | $557,535.60 | Saves $259,653.60 |
| 30 Years | $2,269.97 | $467,189.20 | $817,189.20 | Baseline |
Frequently Asked Questions
What costs are included in PITI mortgage payments?
PITI stands for Principal, Interest, Taxes, and Insurance. While this calculator computes the core Principal and Interest (P&I) based on loan amortization, actual lender escrow accounts frequently add local property taxes, homeowners hazard insurance, and Private Mortgage Insurance (PMI) if your down payment was under 20%.
Why is a 15-year mortgage significantly cheaper overall than a 30-year mortgage?
Because a 15-year term cuts your repayment horizon in half, lenders carry less default risk (often offering lower interest rates), and principal balances amortize twice as fast. On a $350,000 balance at 6.75%, a 15-year mortgage saves more than $259,000 in lifetime interest charges.