Fixed Interest Mortgage Calculator

Reviewed by: Sarah Jones, CFP®

Use this comprehensive fixed interest mortgage calculator to quickly determine your monthly payments, loan principal, required interest rate, or total term based on three known variables. This tool simplifies complex amortization calculations instantly.

Fixed Interest Mortgage Calculator

Detailed Calculation Steps:

Enter inputs and press Calculate to see the steps.

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Fixed Interest Mortgage Calculator Formula

The standard fixed-rate mortgage payment formula is based on the annuity formula, which calculates the monthly payment (M) required to amortize a principal (P) over a term (n) at a fixed monthly interest rate (r).

$$M = P \frac{r(1+r)^n}{(1+r)^n – 1}$$

Where: $r = \frac{\text{Annual Rate}}{1200}$ and $n = \text{Term in Years} \times 12$ (total months).

Formula Source: Investopedia Amortization | Bankrate Payment Formula

Variables

The calculator uses four core variables. You must input three to solve for the fourth:

• Loan Principal (P): The initial amount borrowed from the lender.
• Annual Interest Rate (R): The yearly rate of interest, expressed as a percentage.
• Loan Term (N): The duration of the loan, typically in years (e.g., 15 or 30).
• Monthly Payment (M): The fixed amount paid each month to cover principal and interest.

Related Calculators

Explore these tools for other financial planning needs:

• Amortization Schedule Planner
• Refinance Breakeven Calculator
• Home Equity Line of Credit (HELOC) Cost Estimator
• Property Tax Estimator

What is a Fixed Interest Mortgage Calculator?

A fixed interest mortgage calculator is a crucial financial tool designed to help borrowers estimate the costs associated with a mortgage where the interest rate remains constant for the entire loan term. Unlike adjustable-rate mortgages (ARMs), the predictability of a fixed rate makes this calculator essential for long-term budget planning. It generates a comprehensive amortization schedule showing how the principal is paid down over time.

The primary purpose is to solve the complex annuity equation for one unknown variable, most commonly the required monthly payment (M). This payment amount ensures that the entire principal (P) plus all accrued interest is exactly zeroed out by the final payment date (N). Understanding this fixed monthly liability is the first step toward responsible homeownership.

How to Calculate a Fixed Interest Mortgage (Example)

Let’s find the monthly payment for a $200,000 loan at a 5% annual rate over 30 years.

1. Define Variables: $P = \$200,000$, $R = 5\%$, $N = 30$ years.
2. Convert to Monthly Terms: Monthly rate $r = 0.05 / 12 = 0.0041667$. Total periods $n = 30 \times 12 = 360$ months.
3. Calculate Amortization Factor: Compute the factor $(1+r)^n$. For this example, $(1.0041667)^{360} \approx 4.4677$.
4. Solve for M: Substitute the values into the formula: $$M = \$200,000 \times \frac{0.0041667 \times 4.4677}{4.4677 – 1} \approx \$1,073.64$$

The resulting fixed monthly payment is approximately $1,073.64.

Frequently Asked Questions (FAQ)

Q: What is the difference between a fixed-rate and an adjustable-rate mortgage (ARM)?

A fixed-rate mortgage has an interest rate that remains the same for the entire loan term. An ARM’s rate is locked for an initial period (e.g., 5 years) and then adjusts periodically based on a market index.

Q: Does the monthly payment include property taxes and insurance?

The monthly payment (M) calculated here includes only the principal and interest (P&I). Lenders often require an escrow account for property taxes and homeowner’s insurance (T&I), making the total payment PITI (Principal, Interest, Taxes, Insurance).

Q: Why is the interest rate calculation iterative when solving for R?

When solving for the annual interest rate (R) given P, N, and M, the rate variable is embedded in the exponents, making it impossible to isolate algebraically. Financial calculators use numerical methods like bisection or Newton-Raphson to find an accurate solution.

Q: Can I use this calculator for Canadian or European mortgages?

This calculator uses the US/monthly compounding method. Canadian mortgages typically use semi-annual compounding, which would require a different formula for accurate results.