.apr-calculator-container {
max-width: 600px;
margin: 0 auto;
padding: 20px;
background-color: #f9f9f9;
border: 1px solid #e0e0e0;
border-radius: 8px;
font-family: Arial, sans-serif;
}
.apr-calculator-container h2 {
text-align: center;
color: #333;
}
.apr-input-group {
margin-bottom: 15px;
}
.apr-input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.apr-input-group input {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.apr-btn {
width: 100%;
padding: 12px;
background-color: #0073aa;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
font-weight: bold;
}
.apr-btn:hover {
background-color: #005177;
}
.apr-result {
margin-top: 20px;
padding: 15px;
background-color: #fff;
border: 1px solid #ddd;
border-radius: 4px;
display: none;
}
.apr-result h3 {
margin-top: 0;
color: #2c3e50;
text-align: center;
}
.apr-metric {
display: flex;
justify-content: space-between;
margin-bottom: 10px;
padding-bottom: 10px;
border-bottom: 1px solid #eee;
}
.apr-metric:last-child {
border-bottom: none;
}
.apr-metric span {
font-weight: bold;
}
.highlight-apr {
color: #d35400;
font-size: 1.2em;
}
.apr-content-section {
max-width: 800px;
margin: 40px auto;
font-family: Arial, sans-serif;
line-height: 1.6;
color: #333;
}
.apr-content-section h2 {
color: #0073aa;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
.apr-content-section p {
margin-bottom: 15px;
}
.apr-content-section ul {
margin-bottom: 15px;
}
@media (max-width: 480px) {
.apr-calculator-container {
padding: 15px;
}
}
function calculateAPR() {
// Get Input Values
var principal = parseFloat(document.getElementById('loanPrincipal').value);
var nominalRatePct = parseFloat(document.getElementById('nominalInterest').value);
var years = parseFloat(document.getElementById('loanTerm').value);
var fees = parseFloat(document.getElementById('loanFees').value);
// Validation
if (isNaN(principal) || principal <= 0 || isNaN(nominalRatePct) || isNaN(years) || years <= 0) {
alert("Please enter valid positive numbers for Loan Amount, Interest Rate, and Term.");
return;
}
if (isNaN(fees)) {
fees = 0;
}
// 1. Calculate Standard Monthly Payment based on Nominal Rate
var nominalRateMonthly = nominalRatePct / 100 / 12;
var months = years * 12;
var monthlyPayment = 0;
if (nominalRateMonthly === 0) {
monthlyPayment = principal / months;
} else {
monthlyPayment = principal * (nominalRateMonthly * Math.pow(1 + nominalRateMonthly, months)) / (Math.pow(1 + nominalRateMonthly, months) – 1);
}
// 2. Calculate APR using Iteration (Newton-Raphson method)
// APR is the rate that equates the Net Loan Amount (Principal – Fees) to the stream of payments
var netLoanAmount = principal – fees;
// Initial guess for APR (start with nominal rate)
var guessRate = nominalRateMonthly;
var tolerance = 0.0000001; // Precision
var maxIterations = 100;
var found = false;
// If fees are 0, APR equals nominal rate
if (fees === 0) {
guessRate = nominalRateMonthly;
found = true;
} else if (netLoanAmount <= 0) {
// Edge case: Fees exceed loan amount
alert("Fees cannot be equal to or greater than the loan amount.");
return;
} else {
for (var i = 0; i < maxIterations; i++) {
// Function f(r) = P * (1 – (1+r)^-N) / r – NetAmount
// We need to find r where f(r) = 0
// Present Value of Annuity Formula: PV = PMT * (1 – (1+r)^-n) / r
var r = guessRate;
var powFactor = Math.pow(1 + r, -months);
var fy = (monthlyPayment * (1 – powFactor) / r) – netLoanAmount;
// Derivative f'(r) for Newton-Raphson
// d/dr [ P/r * (1 – (1+r)^-n) ]
// Complex derivative, we can use a simpler secant method or robust binary search if this fails,
// but let's use the explicit derivative for PV formula:
// f'(r) = (P / r^2) * ( (1+r)^(-n-1) * (n*r + 1 + r) – 1 ) — Approximation
// Let's use numeric derivative for simplicity and robustness in a single file
var delta = 0.00001;
var r_plus = r + delta;
var powFactor_plus = Math.pow(1 + r_plus, -months);
var fy_plus = (monthlyPayment * (1 – powFactor_plus) / r_plus) – netLoanAmount;
var derivative = (fy_plus – fy) / delta;
var newRate = r – (fy / derivative);
if (Math.abs(newRate – guessRate) < tolerance) {
guessRate = newRate;
found = true;
break;
}
guessRate = newRate;
}
}
var calculatedAPR = (guessRate * 12 * 100);
var totalCost = (monthlyPayment * months) + fees;
var totalInterest = (monthlyPayment * months) – principal;
// Display Results
document.getElementById('displayApr').innerHTML = calculatedAPR.toFixed(3) + "%";
document.getElementById('displayNominal').innerHTML = nominalRatePct.toFixed(3) + "%";
document.getElementById('displayPayment').innerHTML = "$" + monthlyPayment.toFixed(2);
document.getElementById('displayTotalCost').innerHTML = "$" + totalCost.toFixed(2);
document.getElementById('displayTotalInterest').innerHTML = "$" + totalInterest.toFixed(2);
document.getElementById('resultArea').style.display = "block";
}
Understanding APR Rates and How They Differ from Interest Rates
When shopping for a loan—whether it's a mortgage, auto loan, or personal loan—borrowers are often presented with two different percentages: the interest rate and the Annual Percentage Rate (APR). Understanding the distinction between these two figures is crucial for making informed financial decisions and accurately comparing loan offers from different lenders.
What is APR?
The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing money than the interest rate alone. While the interest rate reflects the cost of borrowing the principal amount, the APR includes both the interest rate and other costs associated with the loan, such as broker fees, discount points, and closing costs, expressed as a yearly percentage.
Because APR accounts for these additional fees, it provides a more comprehensive view of the true cost of the loan. In almost all cases involving closing costs, the APR will be higher than the nominal interest rate.
The Formula Behind the Calculation
While the nominal interest rate is used to calculate your monthly payment, the APR is a derived figure. To calculate it manually is complex because it involves solving for the rate in an annuity formula based on the net amount financed.
Mathematically, the APR finds the discount rate that equates the total stream of future monthly payments to the Net Loan Amount (Principal minus Fees). The logic used in this calculator follows these steps:
- Step 1: Calculate the monthly payment using the principal, nominal interest rate, and loan term.
- Step 2: Subtract all upfront fees (closing costs, points, origination fees) from the loan principal to determine the actual amount of money you receive or the "Net Proceeds."
- Step 3: Calculate the new interest rate that would result in that same monthly payment if the loan amount were only equal to the Net Proceeds.
- Step 4: Convert this periodic rate back to an annual percentage to get the APR.
Why is APR Higher Than the Interest Rate?
APR is higher because it amortizes the upfront costs over the life of the loan. For example, if you borrow $200,000 but pay $5,000 in closing costs, you are effectively paying interest on $200,000 while only receiving $195,000 of value initially. The APR expresses this disparity as a percentage.
If a loan has zero fees, the APR will equal the interest rate.
How to Use This APR Calculator
Use this tool to compare loan offers effectively:
- Loan Amount: Enter the total amount you intend to borrow.
- Nominal Interest Rate: Enter the advertised base interest rate.
- Loan Term: Enter the duration of the loan in years (e.g., 30 for a standard mortgage).
- Total Closing Costs/Fees: Sum up all non-refundable origination fees, points, and closing costs. Do not include prepaid items like taxes or insurance reserves, as these are not considered "costs of borrowing" for APR calculations in the same way.
By comparing the APRs of two different loans, you can see which one is actually cheaper, even if they have different interest rates and fee structures.