Calculating Annual Percentage Rate

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APR Calculator

Calculate the true Annual Percentage Rate by including fees and interest.

Calculated APR

0.00%

What is Annual Percentage Rate (APR)?

The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year. Unlike a standard interest rate, which only accounts for the percentage charged on the principal, the APR incorporates additional costs such as processing fees, insurance, and origination charges. This makes APR a more accurate metric for comparing different financial products.

The Mathematics of APR

To calculate APR manually for a standard installment loan, you need to determine the periodic interest rate that equates the present value of all future payments to the net amount received (Principal minus Fees). The standard formula used by financial institutions involves solving for the internal rate of return (IRR).

For a simplified calculation, you can use the following logic:

  • Step 1: Calculate the total interest paid over the life of the loan.
  • Step 2: Add all upfront fees to the total interest.
  • Step 3: Divide the total cost by the principal.
  • Step 4: Divide by the number of days in the loan term.
  • Step 5: Multiply by 365 and then by 100 to get the percentage.

APR vs. Stated Interest Rate

It is common for lenders to advertise a low interest rate while charging high upfront fees. For example, a loan with a 5% interest rate and $1,000 in fees might actually be more expensive than a loan with a 5.5% interest rate and zero fees. By calculating the APR, you can see the "effective" rate and make an apples-to-apples comparison between lenders.

Example Calculation

Consider a loan of $5,000 with a stated interest rate of 10% over 12 months, and an origination fee of $200.

1. The monthly payment based on 10% interest would be approximately $439.58.
2. Total interest paid over 12 months is $274.96.
3. Total cost = $274.96 (Interest) + $200 (Fees) = $474.96.
4. The APR would be approximately 17.8%, which is significantly higher than the 10% stated rate because the fees are spread over a short term.

function calculateAPRLogic() { var p = parseFloat(document.getElementById('loan_principal').value); var rate = parseFloat(document.getElementById('stated_rate').value); var fees = parseFloat(document.getElementById('extra_fees').value); var months = parseFloat(document.getElementById('loan_term_months').value); var resultDiv = document.getElementById('apr_result_container'); var output = document.getElementById('apr_output'); var breakdown = document.getElementById('apr_breakdown'); if (isNaN(p) || isNaN(rate) || isNaN(months) || p <= 0 || months <= 0) { alert("Please enter valid positive numbers for Principal, Interest, and Term."); return; } if (isNaN(fees)) { fees = 0; } // 1. Calculate the Monthly Payment (PMT) based on the stated rate and principal var monthlyRate = (rate / 100) / 12; var pmt; if (monthlyRate === 0) { pmt = p / months; } else { pmt = (p * monthlyRate) / (1 – Math.pow(1 + monthlyRate, -months)); } // 2. Solve for APR (i) such that: (Principal – Fees) = PMT * [(1 – (1+i)^-n) / i] // We use the Newton-Raphson method to approximate the internal rate of return var amountFinanced = p – fees; var guess = (rate / 100) / 12; // Start with the stated monthly rate as a guess // If rate is 0, start with a tiny guess to avoid division by zero if (guess <= 0) guess = 0.001; var iterations = 20; var precision = 0.0000001; var i = guess; for (var j = 0; j < iterations; j++) { var t1 = Math.pow(1 + i, months); var t2 = Math.pow(1 + i, months – 1); // Function f(i) = AmountFinanced – PMT * ((1 – (1+i)^-n) / i) // We want to find i where f(i) = 0 var f = amountFinanced – (pmt * (1 – Math.pow(1 + i, -months)) / i); // Derivative f'(i) var df = pmt * ( (1 – Math.pow(1 + i, -months)) / Math.pow(i, 2) – (months * Math.pow(1 + i, -months – 1)) / i ); var next_i = i – (f / df); if (Math.abs(next_i – i) < precision) { i = next_i; break; } i = next_i; } var annualAPR = i * 12 * 100; var totalInterest = (pmt * months) – p; var totalCost = totalInterest + fees; output.innerText = annualAPR.toFixed(2) + "%"; breakdown.innerHTML = "Stated Interest Rate: " + rate.toFixed(2) + "%" + "Total Interest: $" + totalInterest.toFixed(2) + "" + "Total Fees: $" + fees.toFixed(2) + "" + "Total Cost of Credit: $" + totalCost.toFixed(2); resultDiv.style.display = "block"; }

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