Mortgage Calculator

Your answer

Your monthly mortgage payment

Start with the home price, your down payment, the rate and the term. The payment appears here with tax and insurance on top, the interest over the whole loan, and how every year splits between interest and the house.

The working

Payment = loan × r ÷ (1 − (1 + r)⁻ⁿ)

Interest is charged each month, so r is the yearly rate split into twelve, and a 30-year mortgage has n = 360 payments.

r = 6.5% ÷ 12 = 0.005417; n = 30 × 12 = 360. Payment = $320,000 × 0.005417 ÷ (1 − (1 + 0.005417)⁻³⁶⁰) = $2,022.62.

Worked examples

• $320,000 at 6.5% for 30 years: $2,022.62 a month, $408,140.64 interest in total.
• $300,000 at 6% for 15 years: $2,531.57 a month, about $155,700 interest, less than half the 30-year total.

Good to know

How to read your mortgage

• Early payments are mostly interest. In year 1 of the $320,000 example, about $20,700 of the $24,271 paid is interest.
• Small extra payments go a long way. Every extra dollar comes straight off the balance, so it stops interest building on that dollar for the rest of the loan.
• Compare the total, not just the monthly amount. A longer term lowers the payment but can double the interest.
• Common mistake: forgetting tax and insurance. Lenders often collect them with the payment, so budget for the full monthly total.
• Rate vs APR. The rate sets the payment. APR also folds in fees, so use APR to compare lenders.

Questions

Questions people ask about mortgages

Printout

Your mortgage summary

One page to take to a lender or broker: your numbers, the monthly breakdown and the balance year by year.

For spreadsheets and code

Check the schedule yourself

principal = 320000
apr = 6.5
months = 360
r = apr / 100 / 12
payment = principal / months if r == 0 else principal * r / (1 - (1 + r) ** -months)
balance = round(principal, 2)
interest_total = 0
for month in range(1, months + 1):
    interest = round(balance * r + 1e-9, 2)
    principal_paid = round(payment - interest + 1e-9, 2)
    if principal_paid >= balance:
        principal_paid = balance
    balance = round(balance - principal_paid + 1e-9, 2)
    interest_total = round(interest_total + interest + 1e-9, 2)
    if balance <= 0:
        break
print(f"payment={payment:.2f}")
print(f"months={month}")
print(f"interest={interest_total:.2f}")

Sources

Where these numbers come from

• CFPB: buying a house
• CFPB: when can I remove PMI from my loan?
• FRED: 30-year fixed mortgage average rate