function calculateAPR() {
var principal = parseFloat(document.getElementById('loanPrincipal').value);
var nominalRate = parseFloat(document.getElementById('loanInterestRate').value);
var termMonths = parseInt(document.getElementById('loanTermMonths').value);
var fees = parseFloat(document.getElementById('totalFees').value);
if (isNaN(principal) || isNaN(nominalRate) || isNaN(termMonths) || isNaN(fees) || termMonths <= 0 || principal <= 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
// Calculate Monthly Payment based on Nominal Interest Rate
var monthlyRate = (nominalRate / 100) / 12;
var payment;
if (monthlyRate === 0) {
payment = principal / termMonths;
} else {
payment = (principal * monthlyRate) / (1 – Math.pow(1 + monthlyRate, -termMonths));
}
// Calculate Total Interest and Cost
var totalRepayment = payment * termMonths;
var totalInterest = totalRepayment – principal;
var totalFinanceCharge = totalInterest + fees;
// APR Calculation (Numerical Iteration – Newton-Raphson or Secant Method)
// We need to find the rate 'r' such that:
// (Principal – Fees) = Payment * [(1 – (1 + r)^-n) / r]
var amountReceived = principal – fees;
var rateGuess = (nominalRate / 100) / 12;
var precision = 0.0000001;
var maxIterations = 1000;
var low = 0;
var high = 1.0;
// Binary search for the effective monthly rate
for (var i = 0; i < maxIterations; i++) {
var mid = (low + high) / 2;
var currentPV = 0;
if (mid === 0) {
currentPV = payment * termMonths;
} else {
currentPV = (payment * (1 – Math.pow(1 + mid, -termMonths))) / mid;
}
if (Math.abs(currentPV – amountReceived) amountReceived) {
low = mid;
} else {
high = mid;
}
rateGuess = mid;
}
var annualAPR = rateGuess * 12 * 100;
document.getElementById('displayAPR').innerText = annualAPR.toFixed(3) + "%";
document.getElementById('displayMonthlyPayment').innerText = "$" + payment.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('displayTotalCost').innerText = "$" + totalFinanceCharge.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('aprResultBox').style.display = "block";
}
Understanding APR Calculation
Annual Percentage Rate (APR) provides a more accurate view of the total cost of borrowing than the base interest rate alone. While the nominal interest rate only accounts for the interest charged on the principal, the APR includes additional costs such as loan origination fees, processing fees, and mortgage insurance.
The APR Formula Logic
The calculation of APR involves finding the internal rate of return (IRR) where the present value of all future loan payments equals the net amount received (Principal minus upfront fees). The formula used for standard amortizing loans is:
Principal – Fees = Σ [ Payment / (1 + i)^n ]
Where i is the monthly interest rate and n is the number of periods. Because the rate exists within the exponent, we use numerical iteration (an algorithmic "guess and check" method) to solve for the exact percentage.
Example Calculation
- Loan Amount: $10,000
- Interest Rate: 5.0%
- Term: 3 years (36 months)
- Upfront Fees: $500
In this scenario, while your nominal rate is 5.0%, your "amount financed" is actually only $9,500 ($10,000 – $500). However, your monthly payments are calculated based on the full $10,000. This discrepancy increases the effective cost of the loan, resulting in a higher APR of approximately 8.54%.
Why APR Matters
Federal law (Truth in Lending Act) requires lenders to disclose the APR so consumers can compare different loan products fairly. A loan with a lower interest rate but very high fees may actually be more expensive than a loan with a slightly higher interest rate and zero fees.