body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-container {
background-color: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 600px) {
.calc-grid {
grid-template-columns: 1fr;
}
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
font-size: 0.9em;
color: #495057;
}
.input-group input {
width: 100%;
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.input-group input:focus {
border-color: #4dabf7;
outline: none;
box-shadow: 0 0 0 3px rgba(77, 171, 247, 0.2);
}
button.calc-btn {
background-color: #228be6;
color: white;
border: none;
padding: 12px 24px;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
font-weight: 600;
width: 100%;
margin-top: 10px;
transition: background-color 0.2s;
}
button.calc-btn:hover {
background-color: #1c7ed6;
}
.results-area {
margin-top: 25px;
padding-top: 20px;
border-top: 2px solid #e9ecef;
}
.result-row {
display: flex;
justify-content: space-between;
margin-bottom: 10px;
padding: 10px;
background: white;
border-radius: 4px;
}
.result-row.highlight {
background-color: #e7f5ff;
border: 1px solid #d0ebff;
}
.result-label {
font-weight: 500;
color: #555;
}
.result-value {
font-weight: 700;
color: #228be6;
}
.article-content {
background: #fff;
padding: 20px;
}
.article-content h2 {
color: #343a40;
margin-top: 30px;
border-bottom: 2px solid #f1f3f5;
padding-bottom: 10px;
}
.article-content p {
margin-bottom: 15px;
color: #495057;
}
.article-content ul {
margin-bottom: 15px;
padding-left: 20px;
}
.article-content li {
margin-bottom: 8px;
}
.info-box {
background-color: #fff9db;
border-left: 4px solid #fab005;
padding: 15px;
margin: 20px 0;
}
function calculateTrueAPR() {
var principal = parseFloat(document.getElementById('principalAmt').value);
var statedRate = parseFloat(document.getElementById('statedRate').value);
var months = parseFloat(document.getElementById('termMonths').value);
var fees = parseFloat(document.getElementById('upfrontFees').value);
// Validation
if (isNaN(principal) || principal <= 0) {
alert("Please enter a valid Principal Amount.");
return;
}
if (isNaN(statedRate) || statedRate < 0) {
alert("Please enter a valid Stated Annual Percentage.");
return;
}
if (isNaN(months) || months <= 0) {
alert("Please enter a valid Duration in months.");
return;
}
if (isNaN(fees) || fees < 0) {
fees = 0;
}
// 1. Calculate Standard Monthly Payment based on Principal and Stated Rate
// Formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
var monthlyRate = statedRate / 100 / 12;
var payment = 0;
if (statedRate === 0) {
payment = principal / months;
} else {
payment = principal * (monthlyRate * Math.pow(1 + monthlyRate, months)) / (Math.pow(1 + monthlyRate, months) – 1);
}
// 2. Determine Amount Financed
// The APR is calculated based on the Amount Financed (Principal – Fees)
// paying off the calculated Payment over the term.
var amountFinanced = principal – fees;
if (amountFinanced <= 0) {
alert("Fees cannot exceed or equal the Principal Amount.");
return;
}
// 3. Iteratively solve for APR using Newton-Raphson or Binary Search
// We need to find rate 'r' such that PV of Payments at rate 'r' equals Amount Financed.
// PV = Payment * (1 – (1+r)^-n) / r
var aprEstimate = 0;
// Binary search approach for stability
var minRate = 0;
var maxRate = 1.0; // 100% monthly rate (extreme upper bound)
var tolerance = 0.0000001;
var foundRate = 0;
for (var i = 0; i amountFinanced) {
// If PV is too high, the discount rate (APR) is too low
minRate = midRate;
} else {
maxRate = midRate;
}
if (Math.abs(pv – amountFinanced) < tolerance) {
foundRate = midRate;
break;
}
foundRate = midRate;
}
var annualAPR = foundRate * 12 * 100;
var totalCost = (payment * months) – principal + fees; // Total cost = Total Payments – Principal + Fees?
// Actually simpler: Total Cost = (Payment * Months) – (Original Principal – Fees) ?
// Let's stick to Total Repayment:
var totalRepayment = payment * months;
// Display Results
document.getElementById('resAPR').innerHTML = annualAPR.toFixed(3) + "%";
document.getElementById('resPayment').innerHTML = "$" + payment.toFixed(2);
document.getElementById('resTotalCost').innerHTML = "$" + totalRepayment.toFixed(2);
document.getElementById('resDiff').innerHTML = (annualAPR – statedRate).toFixed(3) + "%";
document.getElementById('resultsSection').style.display = "block";
}
Understanding APR vs. Stated Rate
The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing money than the stated annual percentage. While the stated rate (often called the nominal rate or base rate) reflects the cost of borrowing the principal amount, the APR includes other costs associated with the transaction, such as broker fees, closing costs, and processing charges.
When comparing financial products, the APR provides a more accurate benchmark because it standardizes the total cost of credit into a single percentage figure. This prevents lenders from advertising a low rate while hiding costs in high upfront fees.
Key Takeaway: If the processing costs are greater than zero, your APR will always be higher than your stated annual percentage. The larger the fees and the shorter the duration, the greater the difference.
How the APR Percentage Rate Calculator Works
This calculator determines the effective APR by treating the "Amount Financed" as the principal minus any upfront costs, while maintaining the monthly payment calculated on the full principal amount. The physics of this calculation involves finding the internal rate of return (IRR) for the cash flow stream.
The logic follows these steps:
- Step 1: Calculate the monthly payment using the full Principal Amount and the Stated Annual Percentage.
- Step 2: Subtract Total Processing Costs from the Principal to find the actual Amount Financed (the net cash you receive).
- Step 3: Use an iterative mathematical formula to find the specific percentage rate that equates the stream of monthly payments back to the net Amount Financed.
- Step 4: Annualize this rate to produce the final APR.
Why is APR Important?
APR is the "true" price tag of a financial obligation. It allows you to compare "apples to apples." For example, consider two offers:
- Offer A: 5.0% Stated Rate with $5,000 in fees.
- Offer B: 5.5% Stated Rate with $0 in fees.
Without an APR calculation, Offer A looks cheaper. However, depending on the duration of the term, Offer A might actually have a significantly higher effective APR once the $5,000 cost is factored in.
Common Inputs Explained
Principal Amount: The total amount of money you are looking to borrow before fees are assessed.
Stated Annual Percentage: The base percentage rate advertised by the lender. This does not include overhead or closing fees.
Duration (Months): The lifespan of the obligation. APR is highly sensitive to time; upfront fees spread over a short term spike the APR significantly compared to a long term.
Total Processing Costs: Any upfront charges, points, origination fees, or closing costs required to finalize the agreement. These are the primary drivers that push the APR above the stated rate.