How to Calculate Mortgage Payments by Hand
Learn the exact fixed-rate mortgage formula lenders use, step through a real example, and see how to add taxes, insurance, and PMI.
The formula lenders actually use
The monthly principal-and-interest payment on a fixed-rate mortgage comes from the amortization formula:
[ M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1} ]
Where:
- M = monthly principal and interest payment
- P = loan amount (home price minus down payment)
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of payments (loan term in years × 12)
This formula assumes the interest rate stays fixed for the life of the loan and that payments are made at the end of each month. It is the same calculation used by virtually every US mortgage lender.
Worked example: $400,000 loan at 6.5% for 30 years
- Loan amount (P): $400,000
- Annual rate: 6.5%, so monthly rate r = 0.065 ÷ 12 = 0.0054167
- Number of payments: 30 × 12 = 360, so n = 360
Plug into the formula:
[ M = 400{,}000 \cdot \frac{0.0054167(1.0054167)^{360}}{(1.0054167)^{360} - 1} ]
[ M \approx 400{,}000 \cdot \frac{0.0054167 \cdot 7.0399}{7.0399 - 1} ]
[ M \approx 400{,}000 \cdot 0.006321 = \mathbf{$2{,}528.40} ]
So the principal-and-interest portion is about $2,528 per month.
Adding taxes, insurance, HOA, and PMI
Your actual monthly housing cost — often called PITI plus HOA — is larger than the principal-and-interest number. Add:
- Property taxes: annual tax ÷ 12
- Homeowners insurance: annual premium ÷ 12
- HOA dues: monthly amount if any
- PMI: typically required when your down payment is below 20%
Continuing the example:
| Cost | Annual | Monthly |
|---|---|---|
| Principal & interest | — | $2,528 |
| Property tax | $4,800 | $400 |
| Insurance | $1,440 | $120 |
| HOA | — | $150 |
| Total monthly PITI + HOA | — | $3,198 |
That extra $670 per month is why lenders care about PITI, not just principal and interest.
Why the formula works
Each monthly payment is split into two parts:
- Interest on the remaining balance.
- Principal that reduces the balance.
Early in the loan, most of the payment goes to interest. Over time, more goes to principal. The amortization formula guarantees the payment stays the same while the interest/principal split shifts gradually.
Common mistakes to avoid
- Using the annual rate directly. Always divide the annual rate by 12.
- Forgetting PMI when putting down less than 20%.
- Ignoring taxes and insurance when budgeting.
- Using a teaser rate instead of the rate you actually qualify for.
Try it instantly
Use our mortgage payment calculator to plug in your own numbers, or build a full amortization schedule to see every payment month by month.