Calculadora de hipotecas
Calcule os pagamentos mensais da hipoteca, os juros totais e o custo total de um empréstimo.
Mortgage Parameters
Advanced Options
Estimated Monthly Payment
Principal amount:
Loan Balance Over Time
Annual Amortization Schedule
| Year | Beg. Balance | Interest Paid | Principal Paid | Remaining Balance |
|---|---|---|---|---|
Step-by-Step Manual Calculation Guide
While our Mortgage Calculator provides instant results and charts, understanding how to compute your monthly payments manually is vital for deep comprehension. Follow this chronological methodology using the standard Amortization formula:
Identify the Loan Parameters
- Principal (P): The total loan amount (Home Price minus Down Payment). (e.g., )
- Annual Interest Rate (r): The yearly interest rate as a decimal. (e.g., % = )
- Number of Months (n): The total number of monthly payments. (e.g., years = months)
Set up the Amortization Formula
Calculate the Core Payment
(1+i)^n, then multiply the numerator, subtract 1 in the denominator, and divide.
For your specific inputs, the calculated Principal & Interest payment is .
Add Escrow and Additional Costs
Final Total Payment = P&I + Taxes + Insurance + PMI + HOA
Result:
Core Mathematical Concepts: How it Works
At its core, a mortgage calculator uses the standard fixed-rate loan amortization formula to determine the monthly payment. This ensures that by the end of the loan term, the principal is fully paid off along with the accumulated interest.
The Amortization Formula
The monthly Principal and Interest (P&I) payment is calculated using the following formula:
Variable Definitions:
- P = Loan Principal Amount The total amount borrowed. This is calculated as the Home Price minus the Down Payment.
-
r = Monthly Interest Rate
The annual interest rate divided by 12 (months) and converted to a decimal. For example, a 6% interest rate means
r = 0.06 / 12 = 0.005. -
n = Total Number of Payments
The number of months in the loan term. For a 30-year term,
n = 30 × 12 = 360monthly payments. - M = Monthly P&I Payment The basic monthly amount paid toward your mortgage principal and interest.
Step-by-Step Manual Calculation Example
Let's walk through a practical scenario where we buy a home priced at $400,000 with a 20% down payment and a 30-year term at an interest rate of 6%.
Compute Down Payment and Loan Principal (P)
Down Payment = $400,000 × 20% = $80,000.
Loan Principal (P) = $400,000 - $80,000 = $320,000.
Determine Monthly Interest Rate (r) & Payments Count (n)
Monthly Rate (r) = 6% / 12 = 0.5% per month = 0.005.
Total Payments (n) = 30 years × 12 months/year = 360.
Plug into the Amortization Formula
Let's calculate the compounding term: (1 + r)^n = (1.005)^360 ≈ 6.022575.
Now plug this back into the formula:
M = $320,000 × [ (0.005 × 6.022575) / (6.022575 - 1) ]
M = $320,000 × [ 0.030113 / 5.022575 ]
M = $320,000 × 0.0059955 ≈ $1,918.56.
Add Advanced Escrow Costs
Real-world monthly payments include other costs which our calculator handles:
- Property Taxes: E.g., 1.2% yearly tax on a $400k home is
($400,000 × 0.012) / 12 = $400.00/mo. - Homeowners Insurance: E.g., $1,200 yearly policy is
$100.00/mo. - PMI (Private Mortgage Insurance): If down payment is under 20%, PMI applies. Since we paid exactly 20%, PMI is $0.
- HOA Fees: Assume homeowner association dues are $0.
PITI: What Makes Up Your Monthly Payment?
Mortgages are often summarized using the acronym PITI (Principal, Interest, Taxes, and Insurance). Understanding how these interact helps you manage long-term finances.
1. Principal & Interest (P&I)
This is the core loan cost. Principal goes toward paying down the actual debt balance, and Interest is the cost paid to the lender. Initially, most of your payment goes to interest; over time, the balance shifts to principal.
2. Property Taxes
Local governments assess taxes on property value. Lenders typically collect this monthly, hold it in an escrow account, and pay the annual tax bill on your behalf.
3. Homeowners Insurance
Protects the property against damage from fires, storms, and other disasters. Lenders require this to protect their collateral. Like taxes, it is paid from escrow.
4. PMI & HOA Dues
PMI: Private Mortgage Insurance protects the lender if you default and is required if your down payment is less than 20%. HOA: Homeowners Association fees are paid separately to manage community facilities.
Expert Tips for Maximum Accuracy
- Factor in extra costs: Real-world monthly housing expenses usually include property taxes, home insurance, and potentially Private Mortgage Insurance (PMI).
- Analyze amortization: Paying even a small extra principal amount each month early in the term can significantly reduce the overall interest paid and shorten the loan life.
- Compare terms: A 15-year mortgage will have higher monthly payments but saves a massive amount of interest over the life of the loan compared to a 30-year option.