This Simple Mortgage Calculator provides a quick and accurate estimate of your monthly principal and interest payments using the standard amortization formula.
Simple Mortgage Calculator Formula
Simple Mortgage Calculator Formula:
M = P [ i(1 + i)ⁿ / (1 + i)ⁿ - 1 ]
Where: i = r / 1200 (Monthly Rate); n = Term in Years * 12 (Total Payments)
Formula Source: Investopedia – Monthly Mortgage Payment Formula | Bankrate – Calculating Mortgage Payment
Variables:
- Principal Loan Amount (P): The total amount of money borrowed (the amount financed).
- Annual Interest Rate (r, %): The yearly rate of interest charged on the loan, expressed as a percentage.
- Loan Term in Years (n): The length of the repayment period in years (e.g., 15 or 30).
- Monthly Payment (M): The fixed amount paid monthly to the lender, covering both principal and interest.
Related Calculators:
- Mortgage Refinance Calculator
- Amortization Schedule Tool
- Down Payment Impact Calculator
- Future Value of Annuity Calculator
What is Simple Mortgage Payment?
The simple monthly mortgage payment (M) is the fixed amount you pay the lender each month to cover the principal and interest charges necessary to fully amortize the loan over the defined term. This calculation is foundational to personal finance, allowing prospective homeowners to budget accurately.
Unlike simple interest calculations, mortgages use compound interest, where the interest is calculated on the remaining principal balance. Early payments are heavily weighted toward interest, while later payments predominantly cover the principal, gradually decreasing the balance to zero by the end of the term.
How to Calculate Simple Monthly Payment (Example):
- Define Variables: Assume a Principal (P) of $300,000, an Annual Rate (r) of 5.0%, and a Term (t) of 30 years.
- Calculate Monthly Rate (i): $i = 0.05 / 12 = 0.0041667$.
- Calculate Total Payments (n): $n = 30 \text{ years} \times 12 \text{ months/year} = 360$.
- Apply Formula Components:
- $A = (1 + i)^n = (1.0041667)^{360} \approx 4.4677$
- Numerator $ = i \times A = 0.0041667 \times 4.4677 \approx 0.018615$
- Denominator $ = A – 1 = 4.4677 – 1 = 3.4677$
- Calculate Monthly Payment (M): $M = P \times (\text{Numerator} / \text{Denominator}) = \$300,000 \times (0.018615 / 3.4677) \approx \$1,610.46$.
Frequently Asked Questions (FAQ):
How does my down payment affect the calculation?
The down payment reduces the Principal Loan Amount (P). A larger down payment means a smaller P, which directly results in a lower monthly payment (M).
What is amortization?
Amortization is the process of paying off a debt over time in regular installments. The schedule shows how much of each payment goes toward interest and how much goes toward reducing the principal balance.
Does this calculator include taxes and insurance?
No, this is a “simple” calculator that only computes the principal and interest (P&I) portion of the payment. Property taxes, homeowners insurance, and PMI (if applicable) are usually added to the P&I payment to form the final escrow payment.
Can I pay off my loan faster?
Yes. By making extra principal payments, you reduce P faster. Since interest is calculated on the remaining P, this shortens the loan term and saves significant money on total interest paid.