Note: This calculation uses an iterative approximation to determine the internal rate of return (IRR) based on total cash outflows versus net capital received.
function calculateCompRate() {
// 1. Get Elements
var capitalInput = document.getElementById("borrowedCapital");
var periodInput = document.getElementById("amortizationPeriod");
var nominalInput = document.getElementById("nominalPercentage");
var upfrontInput = document.getElementById("initialCosts");
var recurringInput = document.getElementById("recurringCosts");
var resultBox = document.getElementById("resultContainer");
var rateDisplay = document.getElementById("finalComparisonRate");
var nominalRepaymentDisplay = document.getElementById("nominalRepaymentResult");
var totalOutflowDisplay = document.getElementById("totalOutflowResult");
var diffDisplay = document.getElementById("diffResult");
// 2. Parse Values
var P = parseFloat(capitalInput.value); // Principal
var N = parseFloat(periodInput.value); // Months
var r_annual = parseFloat(nominalInput.value); // Annual Nominal Rate
var fees_upfront = parseFloat(upfrontInput.value) || 0;
var fees_monthly = parseFloat(recurringInput.value) || 0;
// 3. Validation
if (isNaN(P) || isNaN(N) || isNaN(r_annual) || P <= 0 || N <= 0) {
alert("Please provide valid positive numbers for Capital, Period, and Percentage.");
return;
}
// 4. Calculate Nominal Monthly Payment (Standard Amortization)
var r_monthly = (r_annual / 100) / 12;
var monthly_pmt = 0;
if (r_monthly === 0) {
monthly_pmt = P / N;
} else {
monthly_pmt = P * (r_monthly * Math.pow(1 + r_monthly, N)) / (Math.pow(1 + r_monthly, N) – 1);
}
// 5. Calculate Total Monthly Outflow
var total_monthly_outflow = monthly_pmt + fees_monthly;
// 6. Calculate Comparison Rate using Iteration (Newton-Raphson approximation for IRR)
// We are solving for 'i' (monthly rate) where:
// Net_P = (Total_Outflow / i) * (1 – (1+i)^-N)
// Where Net_P is the amount effectively received (Principal – Upfront Fees)
var net_principal = P – fees_upfront;
// Edge case: if fees eat up all principal
if (net_principal 100%";
resultBox.style.display = "block";
return;
}
var guess_i = r_monthly; // Start with nominal rate as guess
var epsilon = 0.0000001; // Precision
var max_iter = 100;
var found = false;
for (var k = 0; k < max_iter; k++) {
// Function value: f(i) = (Payment/i)*(1-(1+i)^-N) – NetPrincipal
// Derivative: f'(i) … calculating derivative is complex, let's use Secant method or simple Newton
// Simplified Annuity Formula: PV = PMT * [ (1 – (1+i)^-n) / i ]
var pv_guess = 0;
if (guess_i === 0) {
pv_guess = total_monthly_outflow * N;
} else {
pv_guess = total_monthly_outflow * ( (1 – Math.pow(1 + guess_i, -N)) / guess_i );
}
var diff = pv_guess – net_principal;
if (Math.abs(diff) < epsilon) {
found = true;
break;
}
// Derivative approximation (Secant method step logic simplified for stability)
// Calculate PV for a slightly higher rate to estimate slope
var delta = 0.00001;
var guess_i_2 = guess_i + delta;
var pv_guess_2 = total_monthly_outflow * ( (1 – Math.pow(1 + guess_i_2, -N)) / guess_i_2 );
var slope = (pv_guess_2 – pv_guess) / delta;
// Newton step: new_guess = old_guess – f(x)/f'(x)
// Here f(x) is (pv_guess – net_principal)
var new_guess = guess_i – (diff / slope);
if (new_guess < -1) new_guess = -0.99; // prevent crash
guess_i = new_guess;
}
var comparison_annual = guess_i * 12 * 100;
// 7. Display Results
resultBox.style.display = "block";
rateDisplay.innerHTML = comparison_annual.toFixed(2) + "%";
nominalRepaymentDisplay.innerHTML = "$" + monthly_pmt.toFixed(2);
totalOutflowDisplay.innerHTML = "$" + total_monthly_outflow.toFixed(2);
var diff = comparison_annual – r_annual;
diffResult.innerHTML = "+" + diff.toFixed(2) + "% vs Nominal";
}
Understanding How to Calculate a Comparison Rate
When evaluating financial products, the advertised percentage often tells an incomplete story. The Comparison Rate is a mathematical tool used to unify the distinct vectors of financial obligation—specifically the nominal interest, upfront implementation costs, and recurring periodic fees—into a single, comparable percentage metric.
Unlike a standard amortization schedule, calculating a comparison rate requires determining the effective cost of funds. It answers the question: "If all fees were converted into interest, what would that rate be?" This allows borrowers to compare a product with a low nominal rate but high fees against a product with a higher rate but zero fees using a single integer.
The Mathematical Logic
The calculation is derived by solving for the internal rate of return (IRR) of the cash flow stream. The formula equates the "Net Financed Amount" (Capital minus Initial Costs) to the present value of all future "Total Monthly Outflows" (Nominal Repayment plus Periodic Costs).
The equation solved by the calculator above is:
Pnet = Σ [ PMTtotal / (1 + i)t ]
Pnet: The Borrowed Capital minus Initial Implementation Costs.
PMTtotal: The standard amortization repayment plus Recurring Periodic Costs.
i: The periodic comparison rate (which we solve for iteratively).
t: The time period index.
Key Input Variables Defined
Borrowed Capital: The gross amount of credit extended before any deductions.
Amortization Period: The total duration of the obligation, expressed in months (e.g., 25 years = 300 months).
Nominal Annual Percentage: The base rate applied to the principal, excluding ancillary costs.
Initial Implementation Costs: One-off fees such as establishment fees, valuation fees, or settlement fees. These reduce the effective capital received.
Recurring Periodic Costs: Ongoing account keeping fees or service fees added to every repayment cycle.
Why the Result is Always Higher
Mathematically, the Comparison Rate will almost always exceed the Nominal Annual Percentage. This delta represents the friction cost of fees. If the "Effective Cost Difference" in the calculator results is significant (e.g., > 0.5%), it indicates that the fee structure is heavy relative to the capital borrowed. This metric is critical for identifying "low rate" offers that are actually expensive due to high structural costs.
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"@type": "FAQPage",
"mainEntity": [{
"@type": "Question",
"name": "What is the difference between Nominal Percentage and Comparison Rate?",
"acceptedAnswer": {
"@type": "Answer",
"text": "The Nominal Percentage is simply the cost of interest charged on the principal. The Comparison Rate is a derived metric that includes the nominal interest plus all upfront and recurring fees, expressed as a single annualized percentage rate to reveal the true cost of the debt."
}
}, {
"@type": "Question",
"name": "Why does a shorter amortization period increase the Comparison Rate?",
"acceptedAnswer": {
"@type": "Answer",
"text": "When the amortization period is short, upfront costs (Initial Implementation Costs) are amortized over fewer months. This increases their impact on the effective annual rate, causing the Comparison Rate to rise more sharply compared to a longer term where costs are spread out."
}
}, {
"@type": "Question",
"name": "Does this calculator include break costs or early payout fees?",
"acceptedAnswer": {
"@type": "Answer",
"text": "No. Standard comparison rate calculations assume the debt is held for the full amortization period. Contingent costs like early termination fees or late payment penalties are not included in the mathematical formula for comparison rates."
}
}]
}