function calculateAPR() {
// Get values
var principal = parseFloat(document.getElementById('principalAmt').value);
var quotedRate = parseFloat(document.getElementById('statedRate').value);
var years = parseFloat(document.getElementById('termYears').value);
var fees = parseFloat(document.getElementById('closingCosts').value);
// Validation
if (isNaN(principal) || principal <= 0) {
alert("Please enter a valid Principal Amount.");
return;
}
if (isNaN(quotedRate) || quotedRate < 0) {
alert("Please enter a valid Quoted Percentage.");
return;
}
if (isNaN(years) || years <= 0) {
alert("Please enter a valid Duration.");
return;
}
if (isNaN(fees) || fees < 0) {
fees = 0;
}
// Basic Loan Calculations (Amortization)
var months = years * 12;
var monthlyRate = (quotedRate / 100) / 12;
// Calculate standard monthly payment based on quoted rate
var payment = 0;
if (monthlyRate === 0) {
payment = principal / months;
} else {
payment = principal * (monthlyRate * Math.pow(1 + monthlyRate, months)) / (Math.pow(1 + monthlyRate, months) – 1);
}
// APR Calculation Logic (Iterative Newton-Raphson method)
// We need to find the rate 'r' where the Present Value of payments equals (Principal – Fees)
var amountFinanced = principal – fees;
var aprEstimate = monthlyRate; // Initial guess
var tolerance = 0.0000001;
var maxIterations = 100;
var found = false;
// If fees are 0, APR equals quoted rate (roughly)
if (fees === 0) {
aprEstimate = monthlyRate;
found = true;
} else {
// Newton-Raphson iteration
for (var i = 0; i < maxIterations; i++) {
// Function f(r) = Payment * (1 – (1+r)^-N) / r – AmountFinanced
// We solve for f(r) = 0
// Check for r close to 0
var f_value = 0;
var f_derivative = 0;
if (Math.abs(aprEstimate) < 0.00000001) {
// Linear approximation if rate is near 0
f_value = payment * months – amountFinanced;
f_derivative = 0; // Slope undefined/flat here for simple annuity formula, skip 0 case handling for loan APR
} else {
var powTerm = Math.pow(1 + aprEstimate, -months);
f_value = (payment * (1 – powTerm) / aprEstimate) – amountFinanced;
// Derivative f'(r)
var term1 = (payment * months * powTerm) / (aprEstimate * (1 + aprEstimate));
var term2 = (payment * (1 – powTerm)) / (aprEstimate * aprEstimate);
f_derivative = term1 – term2;
}
var newRate = aprEstimate – (f_value / f_derivative);
if (Math.abs(newRate – aprEstimate) < tolerance) {
aprEstimate = newRate;
found = true;
break;
}
aprEstimate = newRate;
}
}
var finalAPR = aprEstimate * 12 * 100;
var totalPayments = payment * months;
var totalCost = totalPayments + fees;
var totalInterest = totalPayments – principal;
// Formatting
document.getElementById('aprOutput').innerHTML = finalAPR.toFixed(3) + "%";
document.getElementById('monthlyPaymentOutput').innerHTML = "$" + payment.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('totalInterestOutput').innerHTML = "$" + totalInterest.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('totalCostOutput').innerHTML = "$" + totalCost.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('result').style.display = "block";
}
Understanding the True Cost of Borrowing
When shopping for financing, the headline number usually advertised is the quoted percentage (often called the nominal rate). However, this number rarely tells the whole story. The **Annual Percentage Rate (APR)** is a broader measure of cost that provides a more accurate picture of what you are actually paying for the privilege of borrowing money.
Why isn't the Quoted Rate the same as APR?
The quoted rate calculates interest based strictly on the principal balance. The APR incorporates **upfront financing costs** (such as origination fees, closing costs, and points) and spreads them over the term of the loan, expressing the total cost as a yearly percentage.
How to Use This Calculator
This tool uses the actuarial method to reverse-engineer the true effective rate of your financing. To get an accurate result, you will need the following details from your Loan Estimate or offer sheet:
Principal Amount: The total amount of money being borrowed before any down payments.
Quoted Annual Percentage: The base rate advertised by the lender.
Duration: How many years you have to repay the debt.
Upfront Financing Costs: The sum of all non-refundable fees required to obtain the financing (e.g., application fees, underwriting fees, discount points).
The Mathematics of APR
While the quoted rate is used to calculate your monthly payment, the APR is derived by treating the "Amount Financed" as the Principal minus Fees.
Imagine you borrow $200,000 at a 4% quoted rate, but you pay $5,000 in fees. You are paying interest on $200,000, but you effectively only received $195,000 in your pocket. The APR calculation asks the mathematical question: "What interest rate would justify monthly payments of $X if the loan amount was only $195,000?" Because the starting amount is lower but the payments remain the same, the resulting percentage (APR) is higher than the quoted rate.
Why is APR Important?
APR is the standard for comparing different lending offers. One lender might offer a low quoted rate but charge high upfront fees. Another might have a slightly higher rate but zero fees. By calculating the APR for both, you normalize these differences and can see which option is mathematically cheaper over the life of the loan.