When you take out a loan, whether it's for a car, a personal expense, or another significant purchase, you'll be making regular payments that cover both the principal amount borrowed and the interest charged by the lender. Understanding how these payments are calculated and what Annual Percentage Rate (APR) truly represents is crucial for making informed financial decisions.
Loan Payment Calculation
The most common method for calculating monthly loan payments is using the amortization formula. This formula ensures that each payment is divided between interest and principal in a way that the loan is fully paid off by the end of its term. The formula for the monthly payment (M) is:
$M = P \frac{r(1+r)^n}{(1+r)^n – 1}$
Where:
P = Principal loan amount
r = Monthly interest rate (Annual interest rate divided by 12 and then by 100)
n = Total number of payments (Loan term in years multiplied by 12)
The total interest paid over the life of the loan is the total amount repaid minus the principal amount borrowed. The total loan cost is the sum of all monthly payments plus any upfront fees.
What is APR?
The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing. It includes not only the nominal interest rate but also most of the fees and other charges associated with the loan. In essence, APR gives you a more accurate picture of the total cost of borrowing money annually.
For a simple loan with no upfront fees, the APR is generally the same as the stated annual interest rate. However, when upfront fees (like origination fees, processing fees, or points) are involved, the APR will be higher than the nominal interest rate because these fees increase the effective cost of the loan.
Calculating the precise APR when fees are involved requires an iterative process or financial software, as it's the interest rate that makes the present value of all loan payments (including fees) equal to the principal amount received. Our calculator approximates the APR by considering the impact of upfront fees on the effective interest paid over the loan's life.
Why Use This Calculator?
Compare Loan Offers: Use it to compare different loan options with varying interest rates and fees.
Budgeting: Understand your monthly financial obligations accurately.
Financial Planning: Make informed decisions about taking on new debt.
Understand Loan Costs: See the true cost of borrowing beyond just the interest rate.
By inputting the loan amount, annual interest rate, loan term in years, and any upfront fees, you can quickly get an estimate of your monthly payments, total interest, total cost, and the effective APR.
function calculateLoanDetails() {
var loanAmount = parseFloat(document.getElementById("loanAmount").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var loanTerm = parseFloat(document.getElementById("loanTerm").value);
var fees = parseFloat(document.getElementById("fees").value);
var monthlyPaymentElement = document.getElementById("monthlyPayment");
var totalInterestElement = document.getElementById("totalInterest");
var totalCostElement = document.getElementById("totalCost");
var aprResultElement = document.getElementById("aprResult");
// Clear previous results
monthlyPaymentElement.textContent = "–";
totalInterestElement.textContent = "–";
totalCostElement.textContent = "–";
aprResultElement.textContent = "–";
// Validate inputs
if (isNaN(loanAmount) || loanAmount <= 0 ||
isNaN(interestRate) || interestRate < 0 ||
isNaN(loanTerm) || loanTerm <= 0 ||
isNaN(fees) || fees 0) {
monthlyPayment = principal * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, numberOfPayments)) / (Math.pow(1 + monthlyInterestRate, numberOfPayments) – 1);
} else {
monthlyPayment = principal / numberOfPayments; // Simple division if interest rate is 0
}
var totalRepayment = monthlyPayment * numberOfPayments;
var totalInterest = totalRepayment – principal;
var totalCost = principal + totalInterest + fees; // Total cost includes principal, interest, and upfront fees
// APR Calculation (Approximation)
// APR is the rate at which the net proceeds of the loan (principal – fees)
// are repaid. We'll find the rate 'i' such that:
// (Principal – Fees) = M * [1 – (1 + i)^-n] / i
// This is hard to solve directly for 'i'. We'll use an iterative method (Newton-Raphson or bisection) or a simpler approximation.
// A common approximation is to treat the fees as reducing the effective principal and then finding the rate.
// Let's try a simpler approach: Calculate the effective APR based on the total paid vs the net received.
// Effective APR = (Total Paid / Net Received – 1) * (12 / Loan Term) — this is a rough estimate
// A more accurate APR calculation requires finding the discount rate that equates future payments to the initial loan amount minus fees.
// Let's use a numerical method for APR if possible, or a good approximation.
// Approximation of APR:
// Find the interest rate 'apr' such that if we received (principal – fees) and paid back
// 'monthlyPayment' for 'numberOfPayments', the total return rate matches the APR.
// It's complex. Let's use a common financial library approach or a simpler iterative search.
// For simplicity, we will use an approximation that reflects the impact of fees.
// A common approximation: Calculate the effective annual rate considering principal, interest, and fees.
// Let's try to find 'apr' such that: (loanAmount – fees) = monthlyPayment * [1 – (1 + monthlyRate_apr)^(-numberOfPayments)] / monthlyRate_apr
// where monthlyRate_apr = apr / 1200
var effectivePrincipal = loanAmount – fees;
if (effectivePrincipal <= 0) {
aprResultElement.textContent = "N/A (Fees exceed loan amount)";
} else {
var low = 0;
var high = 1; // Upper bound for interest rate (e.g., 100% APR)
var apr = 0;
var iterations = 100; // Number of iterations for approximation
for (var i = 0; i 0) {
calculatedPrincipal = monthlyPayment * (1 – Math.pow(1 + monthlyRateApr, -numberOfPayments)) / monthlyRateApr;
} else {
calculatedPrincipal = monthlyPayment * numberOfPayments;
}
if (calculatedPrincipal > effectivePrincipal) {
high = mid;
} else {
low = mid;
}
}
apr = low * 100; // Convert monthly rate to annual percentage
aprResultElement.textContent = apr.toFixed(2);
}
monthlyPaymentElement.textContent = "$" + monthlyPayment.toFixed(2);
totalInterestElement.textContent = "$" + totalInterest.toFixed(2);
totalCostElement.textContent = "$" + totalCost.toFixed(2);
}
function resetForm() {
document.getElementById("loanAmount").value = "20000";
document.getElementById("interestRate").value = "5.5";
document.getElementById("loanTerm").value = "5";
document.getElementById("fees").value = "100";
document.getElementById("monthlyPayment").textContent = "–";
document.getElementById("totalInterest").textContent = "–";
document.getElementById("totalCost").textContent = "–";
document.getElementById("aprResult").textContent = "–";
}
// Initial calculation on page load if default values are present
window.onload = function() {
calculateLoanDetails();
};