# Mortgage Calculator

- **URL:** https://codeasystem.com/calculators/finance/mortgage-calculator/
- **Category:** finance
- **Description:** Estimate the monthly principal-and-interest payment on a fixed-rate home loan, plus total interest and a year-by-year amortization schedule.
- **Primary output:** Estimated monthly payment (P&I): $2,275.44

## Inputs
- Home price (name: `price`, type: number, prefix: $, example: 450000)
- Down payment (name: `down`, type: number, prefix: $, example: 90000)
- Interest rate (name: `rate`, type: number, example: 6.5)
- Loan term (name: `term`, type: number, example: 30)

## Outputs
- Estimated monthly payment (P&I): $2,275.44
- Loan amount: $360,000.00
- Total of payments: $819,160.16
- Total interest: $459,160.16
- Payoff time: 360 months (30 years)

## Formula / methodology
```
M = P · r / (1 − (1 + r)^−n)
P = loan amount   r = monthly rate (APR ÷ 12)   n = months
```

The standard fixed-rate mortgage payment comes from the amortizing loan formula above. Each month, interest accrues on the remaining balance at the annual rate divided by 12; whatever part of your payment is not interest reduces the principal. Early payments are mostly interest, while late payments are mostly principal; which is why the schedule below shifts over time.

Total interest is simply the sum of every payment minus the amount you borrowed.

## Assumptions & limitations
- Fixed interest rate for the whole term.
- Principal and interest only; property tax, homeowners insurance, HOA fees and PMI are not included.
- Payments are made monthly and on time.
- No extra principal payments are modeled.

## How to use
1. **Enter the price and down payment**; Use the purchase price and the cash you plan to put down. A 20% down payment avoids PMI on most conventional loans.
2. **Add the rate and term**; Enter the quoted APR and the term in years; 30 and 15 are the most common.
3. **Read the result and schedule**; The main number is your monthly principal-and-interest payment; the table shows how the balance falls each year.

## Example
For a $450,000 home with a $90,000 down payment, a 6.5% APR and a 30-year term, you finance $360,000 and pay $2,275.44 per month in principal and interest; about $459,160 of it as interest over 30 years.

Result for these inputs:

```
Estimated monthly payment (P&I): $2,275.44
```

## About this calculator
### What a mortgage payment actually covers

Lenders talk about PITI: principal, interest, taxes and insurance. This calculator models the PI part. Your real escrowed payment will usually be higher once property taxes, homeowners insurance and possibly PMI or HOA dues are added, so treat the result as the loan-only floor of your housing cost.

### Why the term matters so much

A shorter term raises the required payment but slashes total interest, because you borrow the money for less time. On a large balance the difference between a 15-year and 30-year loan is often hundreds of thousands of dollars in interest.

### Small rate changes, big effects

Because payments compound over hundreds of months, each 0.25% move in the rate changes the payment by several dollars per $100,000 borrowed; and can change lifetime interest by tens of thousands.

## FAQs
### Does this include property tax and insurance?

No. The result is principal and interest only. Add your estimated yearly property tax and insurance divided by 12 to approximate your full escrowed payment.

### How much down payment do I need?

Conventional loans often require 3–5% minimum, but 20% avoids private mortgage insurance (PMI). FHA loans allow lower down payments with mortgage insurance premiums.

### Can I see the effect of paying extra?

This version does not model extra payments. As a rough rule, adding one extra monthly payment per year to a 30-year loan shortens it by about 4–6 years depending on the rate.

### Is the amortization table exact?

Yes for a fixed-rate loan with no extra payments; it applies the same rounding conventions lenders use, so small cent-level differences from your lender’s statement are possible.

> **Disclaimer:** This calculator is for general educational purposes only and does not constitute professional advice.

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Last updated: 2026-08-23 · Version: 1.0.0 · [HTML version](https://codeasystem.com/calculators/finance/mortgage-calculator/)