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Estimated APR (Nominal)0.00%
Monthly Payment$0.00
Total Interest Payable$0.00
Total Amount Repayable$0.00
Effective Difference0.00%
Understanding Flat Rate vs. APR
When shopping for car finance or personal loans, you may encounter two different types of interest rates: the Flat Rate and the APR (Annual Percentage Rate). While a Flat Rate often looks lower and more attractive, it can be misleading regarding the true cost of borrowing.
The Flat Rate to APR Calculator above allows you to convert a quoted flat interest rate into the equivalent APR, helping you compare loan offers accurately.
What is a Flat Rate?
A Flat Rate calculates interest on the original principal amount for the entire duration of the loan, regardless of how much you have already paid back. This means you pay interest on money you no longer owe in the later years of the loan term.
Example: If you borrow $10,000 at a 5% Flat Rate for 4 years, you pay 5% of $10,000 ($500) every year in interest, totaling $2,000, even though your balance decreases every month.
What is APR?
The Annual Percentage Rate (APR), specifically in the context of reducing balance loans, calculates interest based on the outstanding balance. As you pay down the principal, the amount of interest you pay decreases. APR is the standard metric for comparing financial products because it reflects the true cost of funds.
Why is the Flat Rate lower than the APR?
Because the Flat Rate charges interest on the full starting amount, a "5% Flat Rate" usually results in roughly the same monthly payment as a "9-10% APR." This discrepancy occurs because the APR formula accounts for the fact that, on average, you only owe about half the principal over the life of the loan.
How the Calculation Works
Converting Flat Rate to APR involves determining the Monthly Payment first, and then reverse-engineering the effective interest rate (IRR) that equates that payment to the loan amount:
Step 1: Calculate Total Interest = Principal × Flat Rate × (Years).
Step 2: Calculate Total Repayable = Principal + Total Interest.
Step 3: Calculate Monthly Payment = Total Repayable / Months.
Step 4: Use an iterative financial formula (Newton-Raphson or Binary Search) to find the APR that results in that specific Monthly Payment on a reducing balance basis.
function calculateFlatToAPR() {
// 1. Get DOM elements
var elAmount = document.getElementById("fr_loanAmount");
var elRate = document.getElementById("fr_flatRate");
var elTerm = document.getElementById("fr_term");
var elResults = document.getElementById("fr_results");
var elError = document.getElementById("fr_error");
var elResApr = document.getElementById("res_apr");
var elResMonthly = document.getElementById("res_monthly");
var elResTotalInterest = document.getElementById("res_totalInterest");
var elResTotalAmount = document.getElementById("res_totalAmount");
var elResDiff = document.getElementById("res_diff");
// 2. Parse values
var principal = parseFloat(elAmount.value);
var flatRatePercent = parseFloat(elRate.value);
var months = parseInt(elTerm.value);
// 3. Validation
if (isNaN(principal) || isNaN(flatRatePercent) || isNaN(months) || principal <= 0 || flatRatePercent < 0 || months <= 0) {
elError.style.display = "block";
elResults.style.display = "none";
return;
}
elError.style.display = "none";
// 4. Calculate Flat Rate Metrics
// Flat Interest = Principal * (Rate/100) * (Months/12)
var years = months / 12;
var totalInterest = principal * (flatRatePercent / 100) * years;
var totalRepayable = principal + totalInterest;
var monthlyPayment = totalRepayable / months;
// 5. Calculate APR using Binary Search (Finding the reducing balance rate)
// We need to find monthly rate 'r' such that:
// Principal = (MonthlyPayment / r) * (1 – (1 + r)^(-months))
var foundRate = 0;
// Edge case: if rate is 0
if (flatRatePercent === 0) {
foundRate = 0;
} else {
var min = 0;
var max = 1.0; // 100% monthly rate (absurdly high upper bound)
var tolerance = 0.0000001;
// Binary search for the rate
for (var i = 0; i < 100; i++) {
var mid = (min + max) / 2;
if (mid === 0) {
// avoid division by zero if mid hits 0
min = mid;
continue;
}
// Calculate PMT required for this 'mid' rate to match Principal
// Formula: PMT = P * ( r * (1+r)^N ) / ( (1+r)^N – 1 )
var factor = Math.pow(1 + mid, months);
var calcPmt = principal * (mid * factor) / (factor – 1);
if (Math.abs(calcPmt – monthlyPayment) < tolerance) {
foundRate = mid;
break;
}
if (calcPmt < monthlyPayment) {
// If calculated payment at this rate is too low, we need a higher rate
min = mid;
} else {
max = mid;
}
foundRate = mid;
}
}
// Convert monthly rate to Annual Nominal APR
var apr = foundRate * 12 * 100;
var difference = apr – flatRatePercent;
// 6. Formatting Helper
function formatMoney(num) {
return "$" + num.toLocaleString("en-US", { minimumFractionDigits: 2, maximumFractionDigits: 2 });
}
// 7. Update UI
elResApr.innerHTML = apr.toFixed(2) + "%";
elResMonthly.innerHTML = formatMoney(monthlyPayment);
elResTotalInterest.innerHTML = formatMoney(totalInterest);
elResTotalAmount.innerHTML = formatMoney(totalRepayable);
// Show how much higher APR is than Flat Rate
elResDiff.innerHTML = "+" + difference.toFixed(2) + "%";
elResults.style.display = "block";
}