Your quoted Flat Rate is 0%, but the actual cost of borrowing (APR) is 0%.
Understanding Flat Rate vs. APR
When shopping for car finance or personal loans, you will often encounter two very different types of interest rate figures: the Flat Rate and the Annual Percentage Rate (APR). Confusing the two can lead to paying significantly more interest than expected.
The Golden Rule: A Flat Rate always looks lower than the equivalent APR. A 5% Flat Rate is roughly equivalent to a 10% APR.
What is a Flat Rate?
A Flat Rate calculates interest on the original loan amount for the entire duration of the term, regardless of how much you have paid back. It does not account for the fact that your principal balance decreases with every monthly payment.
For example, if you borrow 10,000 at a 5% flat rate for 3 years:
Interest per year: 5% of 10,000 = 500
Total Interest: 500 × 3 years = 1,500
Total Payable: 11,500
What is APR?
APR (Annual Percentage Rate) is the standard method for comparing financial products. It calculates interest based on the declining balance of the loan. As you pay off the principal, you pay less interest.
Because the Flat Rate charges interest on money you have already paid back, the "True" interest rate (APR) is mathematically much higher. This calculator converts that misleading flat rate into the standard APR so you can compare it effectively with bank loans or other finance options.
How the Calculation Works
The conversion requires determining the internal rate of return (IRR) of the cash flows. While the flat rate uses simple multiplication (Principal × Rate × Years), the APR formula solves for the rate r where the present value of all monthly payments equals the loan amount minus any upfront fees.
function calculateApr() {
var principal = parseFloat(document.getElementById('principal').value);
var flatRate = parseFloat(document.getElementById('flatRate').value);
var months = parseInt(document.getElementById('months').value);
var fees = parseFloat(document.getElementById('fees').value);
// Validation
if (isNaN(principal) || principal <= 0) {
alert("Please enter a valid borrowed amount.");
return;
}
if (isNaN(flatRate) || flatRate < 0) {
alert("Please enter a valid flat rate.");
return;
}
if (isNaN(months) || months <= 0) {
alert("Please enter a valid duration in months.");
return;
}
if (isNaN(fees)) {
fees = 0;
}
// 1. Calculate Flat Rate Metrics
var years = months / 12;
var totalInterestFlat = principal * (flatRate / 100) * years;
var totalPayable = principal + totalInterestFlat + fees;
var monthlyPayment = totalPayable / months;
// 2. Calculate APR using Bisection Method (finding rate for declining balance)
// We need to find rate 'r' (monthly) such that:
// Principal = (MonthlyPayment / r) * (1 – (1+r)^(-months))
// Note: APR calculations usually factor fees into the cost.
// The cash flow is: Receive Principal (minus fees usually, but here fees are added to total payable, implies financed fees).
// Let's assume standard consumer finance: Principal is received. Payments are made.
// If fees are paid upfront, the effective principal received is (Principal – Fees).
// If fees are added to the loan, the Monthly Payment increases (already handled above), and Principal is just Principal.
// We will stick to the cash flow: Loan Amount vs Stream of Monthly Payments.
var effectivePrincipal = principal; // Assuming fees are rolled into the loan payments calculated above
var minRate = 0;
var maxRate = 1.0; // 100% monthly rate (extreme upper bound)
var estimatedMonthlyRate = 0;
var epsilon = 0.0000001;
// Bisection search for rate
for (var i = 0; i < 100; i++) {
var midRate = (minRate + maxRate) / 2;
if (midRate === 0) {
estimatedMonthlyRate = 0;
break;
}
// Calculate PMT required for this midRate to pay off effectivePrincipal
// Formula: P = (r * PV) / (1 – (1+r)^-n)
var calcPmt = (midRate * effectivePrincipal) / (1 – Math.pow(1 + midRate, -months));
if (Math.abs(calcPmt – monthlyPayment) < epsilon) {
estimatedMonthlyRate = midRate;
break;
}
if (calcPmt < monthlyPayment) {
// Rate is too low
minRate = midRate;
} else {
maxRate = midRate;
}
estimatedMonthlyRate = midRate;
}
var annualRate = estimatedMonthlyRate * 12 * 100;
// Display Results
document.getElementById('resMonthly').innerText = monthlyPayment.toFixed(2);
document.getElementById('resTotal').innerText = totalPayable.toFixed(2);
document.getElementById('resInterest').innerText = (totalInterestFlat + fees).toFixed(2);
document.getElementById('resApr').innerText = annualRate.toFixed(2) + "%";
document.getElementById('resFlatVal').innerText = flatRate.toFixed(2) + "%";
document.getElementById('resAprVal').innerText = annualRate.toFixed(2) + "%";
document.getElementById('result-area').style.display = "block";
}