Determine the effective annual cost of borrowing including fees.
$
%
Years
$
Calculated Real APR:0.00%
Monthly Payment (Principal + Rate):$0.00
Effective Cost Difference:0.00%
Total Cost of Borrowing:$0.00
function calculateTrueAPR() {
// 1. Get Inputs by exact IDs
var principalInput = document.getElementById('aprPrincipal').value;
var nominalInput = document.getElementById('aprNominal').value;
var termInput = document.getElementById('aprTerm').value;
var feesInput = document.getElementById('aprFees').value;
// 2. Validate and Parse
var P = parseFloat(principalInput); // Principal
var R = parseFloat(nominalInput); // Nominal Rate
var N_years = parseFloat(termInput); // Term in years
var Fees = parseFloat(feesInput); // Upfront Fees
if (isNaN(P) || P <= 0) {
alert("Please enter a valid Principal Amount.");
return;
}
if (isNaN(R) || R < 0) {
alert("Please enter a valid Stated Annual Percentage.");
return;
}
if (isNaN(N_years) || N_years <= 0) {
alert("Please enter a valid Repayment Term.");
return;
}
if (isNaN(Fees) || Fees < 0) {
Fees = 0; // Default to 0 if empty
}
// 3. Logic: Calculate Monthly Payment based on Nominal Rate
// Monthly Interest Rate (decimal)
var i = (R / 100) / 12;
// Total Months
var n = N_years * 12;
var monthlyPayment = 0;
if (i === 0) {
monthlyPayment = P / n;
} else {
// Standard Annuity Formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
monthlyPayment = P * (i * Math.pow(1 + i, n)) / (Math.pow(1 + i, n) – 1);
}
// 4. Logic: Calculate APR
// APR is the rate that equates the Adjusted Principal (P – Fees) to the stream of payments
var adjustedPrincipal = P – Fees;
if (adjustedPrincipal <= 0) {
alert("Fees cannot equal or exceed the Principal amount.");
return;
}
// We need to find 'r' (monthly) such that:
// adjustedPrincipal = monthlyPayment * (1 – (1+r)^-n) / r
// Uses Bisection Method for robust convergence
var minRate = 0;
var maxRate = 100; // 10000% annual
var tolerance = 0.0000001;
var foundRate = 0;
var iteration = 0;
// Loop to approximate rate
while (iteration < 100) {
var midRate = (minRate + maxRate) / 2;
var monthlyDec = midRate / 12;
var calculatedP = 0;
if (monthlyDec === 0) {
calculatedP = monthlyPayment * n;
} else {
calculatedP = monthlyPayment * (1 – Math.pow(1 + monthlyDec, -n)) / monthlyDec;
}
// Check difference
if (Math.abs(calculatedP – adjustedPrincipal) adjustedPrincipal) {
// Rate is too low (Present Value is too high)
minRate = midRate;
} else {
// Rate is too high (Present Value is too low)
maxRate = midRate;
}
foundRate = midRate;
iteration++;
}
var aprValue = foundRate * 100; // Annualize
// Total Cost Calculation
var totalPayments = monthlyPayment * n;
var totalCost = totalPayments – P + Fees;
// 5. Display Results
document.getElementById('resultAPR').innerHTML = aprValue.toFixed(3) + '%';
document.getElementById('resultPayment').innerHTML = '$' + monthlyPayment.toFixed(2);
var diff = aprValue – R;
document.getElementById('resultDiff').innerHTML = '+' + diff.toFixed(3) + '%';
document.getElementById('resultTotalCost').innerHTML = '$' + totalCost.toFixed(2);
// Show results div
document.getElementById('aprResults').style.display = "block";
}
How to Calculate APR (Annual Percentage Rate)
Calculating the Annual Percentage Rate (APR) is a critical step in assessing the true cost of a loan or credit agreement. Unlike the "Stated Annual Percentage" (or nominal rate), which only reflects the interest charged on the principal, the APR incorporates the impact of upfront fees, closing costs, and finance charges spread over the life of the loan. This provides a standardized metric for comparing different financial products.
The Mathematics of APR
The calculation of APR is effectively an internal rate of return (IRR) calculation. It solves for the interest rate that equates the net amount financed (Loan Principal minus Fees) with the future stream of monthly payments.
The logic follows these specific steps:
Calculate the Monthly Payment: First, determine the periodic payment amount based on the full principal ($P$) and the stated nominal rate ($r$).
Determine Adjusted Principal: Subtract all origination fees, points, and closing costs ($F$) from the principal amount to find the actual amount of money received ($P_{adj} = P – F$).
Solve for the Rate: Using numerical methods (such as the bisection method used in the calculator above), solve for the new rate that makes the present value of the monthly payments equal to the Adjusted Principal.
Annualize: Multiply the resulting periodic rate by the number of periods in a year (12 for monthly payments) to get the APR.
The Equation:
Padj = PMT × [ (1 – (1 + i)-n) / i ]
Where:
Padj = Principal minus Fees
PMT = Monthly Payment derived from Nominal Rate
n = Total number of months
i = The periodic APR (which we solve for)
Why Fees Increase APR
When you pay upfront fees, you are effectively borrowing less money than the stated principal, yet you are still making payments based on the full principal amount. This discrepancy increases the effective yield to the lender, which is why the APR is almost always higher than the stated annual percentage.
For example, if you borrow $200,000 at 5% but pay $5,000 in fees, you only receive $195,000. However, your monthly payments are calculated on $200,000. The APR calculation reveals the interest rate required to generate those same payments if the loan amount was actually just $195,000.
When APR Equals the Stated Rate
If there are zero fees (no origination charges, closing costs, or points), the Adjusted Principal equals the original Principal. in this specific mathematical scenario, the APR will be identical to the Stated Annual Percentage.