Amortized Loan Calculator
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Amortized Loan Calculator
Payment Summary
Enter loan details to see your payment information.
Your estimated monthly payment, total interest, and amortization schedule will appear here.
Understanding Amortized Loans and the Calculator
An amortized loan is a type of loan where each payment you make consists of both principal and interest. Over the life of the loan, the proportion of interest paid decreases with each payment, while the proportion of principal repayment increases. This process is called amortization. Common examples include mortgages, auto loans, and personal loans.
How the Calculator Works
This calculator helps you estimate your loan payments based on the principal amount, annual interest rate, loan term, and payment frequency. It uses a standard loan amortization formula to determine your regular payment amount.
The Amortization Formula
The formula for calculating the periodic payment (M) of an amortized loan is derived from the present value of an annuity formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Periodic Payment (the amount you pay each period)P = Principal Loan Amount (the total amount borrowed)i = Periodic Interest Rate (the annual rate divided by the number of payment periods per year)n = Total Number of Payments (the loan term in years multiplied by the number of payment periods per year)
Step-by-Step Calculation Breakdown:
- Calculate Periodic Interest Rate (i): The annual interest rate is divided by the number of payments made per year. For example, a 5% annual rate with monthly payments (12 per year) results in a periodic rate of
0.05 / 12.
- Calculate Total Number of Payments (n): The loan term in years is multiplied by the number of payments per year. A 30-year loan with monthly payments has
30 * 12 = 360 total payments.
- Apply the Formula: These values (
i and n) are plugged into the main formula along with the principal (P) to find the periodic payment (M).
- Calculate Total Paid and Total Interest: The total amount repaid is
M * n. The total interest paid is (M * n) - P.
Using the Calculator
Simply input the required figures into the fields:
- Loan Amount: The total sum you are borrowing.
- Annual Interest Rate: The yearly interest rate, expressed as a percentage.
- Loan Term: The duration of the loan, in years.
- Payment Frequency: How often you will make payments (monthly, bi-weekly, weekly).
Click "Calculate Payments" to see your estimated periodic payment, the total amount you'll repay over the loan's life, and the total interest incurred. This tool is invaluable for budgeting and understanding the financial commitment of taking out a loan.
Example Scenario:
Let's say you're taking out a loan of $200,000 with an annual interest rate of 6%, a loan term of 30 years, and you plan to make monthly payments.
- Principal (P) = $200,000
- Annual Interest Rate = 6% (0.06)
- Loan Term = 30 years
- Payment Frequency = Monthly (12)
Calculations:
- Periodic Interest Rate (i) = 0.06 / 12 = 0.005
- Total Number of Payments (n) = 30 * 12 = 360
Using the formula, the estimated monthly payment (M) would be approximately $1,199.10.
Over 30 years, you would make 360 payments of $1,199.10, totaling $431,676.00.
The total interest paid would be $431,676.00 – $200,000 = $231,676.00.
function calculateAmortization() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var loanTermYears = parseFloat(document.getElementById("loanTermYears").value);
var paymentFrequency = parseInt(document.getElementById("paymentFrequency").value);
var resultDiv = document.getElementById("result");
// Input validation
if (isNaN(principal) || principal <= 0) {
resultDiv.innerHTML = "Please enter a valid loan amount.";
return;
}
if (isNaN(annualRate) || annualRate < 0) {
resultDiv.innerHTML = "Please enter a valid annual interest rate.";
return;
}
if (isNaN(loanTermYears) || loanTermYears <= 0) {
resultDiv.innerHTML = "Please enter a valid loan term in years.";
return;
}
if (isNaN(paymentFrequency) || paymentFrequency <= 0) {
resultDiv.innerHTML = "Please select a valid payment frequency.";
return;
}
var monthlyRate = annualRate / 100 / paymentFrequency;
var numberOfPayments = loanTermYears * paymentFrequency;
var monthlyPayment = 0;
var totalPaid = 0;
var totalInterest = 0;
if (monthlyRate === 0) { // Handle zero interest rate case
monthlyPayment = principal / numberOfPayments;
totalPaid = monthlyPayment * numberOfPayments;
totalInterest = 0;
} else {
// Calculate monthly payment using the amortization formula
var numerator = monthlyRate * Math.pow(1 + monthlyRate, numberOfPayments);
var denominator = Math.pow(1 + monthlyRate, numberOfPayments) – 1;
monthlyPayment = principal * (numerator / denominator);
totalPaid = monthlyPayment * numberOfPayments;
totalInterest = totalPaid – principal;
}
// Format the results
var formattedMonthlyPayment = monthlyPayment.toLocaleString(undefined, { style: 'currency', currency: 'USD' });
var formattedTotalPaid = totalPaid.toLocaleString(undefined, { style: 'currency', currency: 'USD' });
var formattedTotalInterest = totalInterest.toLocaleString(undefined, { style: 'currency', currency: 'USD' });
resultDiv.innerHTML =
formattedMonthlyPayment +
"
Estimated Periodic Payment";
// Optionally display more details
resultDiv.innerHTML += "" +
formattedTotalPaid +
"
Total Amount to be Repaid";
resultDiv.innerHTML += "" +
formattedTotalInterest +
"
Total Estimated Interest Paid";
}