Calculating Inflation Rate with Nominal and Real Interest Rate

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Mortgage Payment Calculator

Understanding Your Mortgage Payment

A mortgage is a significant financial commitment, and understanding how your monthly payment is calculated is crucial. The primary components that determine your mortgage payment are the loan amount, the annual interest rate, and the loan term (the number of years you have to repay the loan).

The Mortgage Payment Formula

The standard formula used to calculate a fixed-rate mortgage payment is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

  • M = Your total monthly mortgage payment
  • P = The principal loan amount (the amount you borrowed)
  • i = Your monthly interest rate (annual rate divided by 12)
  • n = The total number of payments over the loan's lifetime (loan term in years multiplied by 12)

Key Terms Explained

  • Principal (P): This is the amount of money you borrow from the lender to purchase your home.
  • Annual Interest Rate: This is the percentage charged by the lender for borrowing the money. It's expressed as a yearly rate.
  • Monthly Interest Rate (i): To use in the formula, the annual interest rate must be converted to a monthly rate by dividing it by 12. For example, a 6% annual rate becomes 0.06 / 12 = 0.005 monthly.
  • Loan Term: This is the duration of the loan, usually expressed in years (e.g., 15, 20, or 30 years).
  • Total Number of Payments (n): This is calculated by multiplying the loan term in years by 12 (the number of months in a year). A 30-year mortgage will have 30 * 12 = 360 payments.

Example Calculation

Let's say you're looking to buy a home and need a mortgage with the following details:

  • Loan Amount (P): $250,000
  • Annual Interest Rate: 5%
  • Loan Term: 30 years

First, we need to calculate the monthly interest rate (i) and the total number of payments (n):

  • Monthly Interest Rate (i) = 5% / 12 = 0.05 / 12 = 0.00416667
  • Total Number of Payments (n) = 30 years * 12 months/year = 360

Now, plugging these values into the formula:

M = 250000 [ 0.00416667(1 + 0.00416667)^360 ] / [ (1 + 0.00416667)^360 – 1]

M = 250000 [ 0.00416667 * (1.00416667)^360 ] / [ (1.00416667)^360 – 1]

M = 250000 [ 0.00416667 * 4.467744 ] / [ 4.467744 – 1]

M = 250000 [ 0.0186156 ] / [ 3.467744 ]

M = 4653.90 / 3.467744

M ≈ $1,342.05

This means your estimated monthly principal and interest payment for this mortgage would be approximately $1,342.05. Keep in mind that this calculation typically only includes principal and interest. Your actual monthly housing expense will likely be higher as it often includes property taxes, homeowner's insurance (forming an PITI payment), and potentially private mortgage insurance (PMI).

function calculateMortgage() { var loanAmount = parseFloat(document.getElementById("loanAmount").value); var interestRate = parseFloat(document.getElementById("interestRate").value); var loanTerm = parseFloat(document.getElementById("loanTerm").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(loanAmount) || isNaN(interestRate) || isNaN(loanTerm) || loanAmount <= 0 || interestRate < 0 || loanTerm <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for all fields."; return; } var monthlyInterestRate = interestRate / 100 / 12; var numberOfPayments = loanTerm * 12; // Calculate monthly payment using the formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1] var numerator = monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments); var denominator = Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1; if (denominator === 0) { // Avoid division by zero, though unlikely with valid inputs resultDiv.innerHTML = "Calculation error. Please check inputs."; return; } var monthlyPayment = loanAmount * (numerator / denominator); // Format the result to two decimal places var formattedMonthlyPayment = monthlyPayment.toFixed(2); resultDiv.innerHTML = "Your estimated monthly mortgage payment (Principal & Interest) is: $" + formattedMonthlyPayment + ""; }

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