How loan EMI is calculated: the formula, a JS implementation, and an amortization table

Every loan app shows an EMI (equated monthly installment). The formula looks intimidating, but it's simple once you see where it comes from. Here's the math, an implementation, and a month-by-month breakdown.

The formula

EMI = P × r × (1 + r)^n / ((1 + r)^n − 1)

• P = principal (loan amount)
• r = monthly interest rate (annual rate ÷ 12 ÷ 100)
• n = number of monthly payments

The result is a fixed payment where the balance reaches exactly zero after n payments.

Implementation

function calculateEmi(principal, annualRatePercent, years) {
  const n = years * 12;
  const r = annualRatePercent / 12 / 100;

  // Edge case: 0% interest would divide by zero in the formula
  if (r === 0) return principal / n;

  const factor = Math.pow(1 + r, n);
  return (principal * r * factor) / (factor - 1);
}

console.log(calculateEmi(1_000_000, 9, 20).toFixed(2));
// ≈ 8997.9 per month

On ₹10,00,000 at 9% for 20 years, you pay about ₹21.6 lakh in total, so more than half of that is interest.

Where the money actually goes: amortization

Each month, interest is charged on the remaining balance, and whatever is left of the EMI reduces the principal.

function amortize(principal, annualRatePercent, years) {
  const r = annualRatePercent / 12 / 100;
  const n = years * 12;
  const emi = calculateEmi(principal, annualRatePercent, years);

  let balance = principal;
  const rows = [];

  for (let month = 1; month <= n; month++) {
    const interest = balance * r;
    const principalPaid = emi - interest;
    balance -= principalPaid;
    rows.push({ month, interest, principalPaid, balance: Math.max(balance, 0) });
  }
  return rows;
}

In the first month of the example above, about ₹7,500 goes to interest and only about ₹1,500 reduces the loan. This is why early prepayments save so much: they cut the balance that interest is calculated on.

Edge cases to handle

• Zero rate: guard against division by zero, as above.
• Floating-point drift: the final balance may be a tiny non-zero number. Clamp it, and round only for display.
• Invalid input: negative or empty values should return an error, not NaN.
• Real lenders differ slightly: rounding rules, processing fees, and daily vs. monthly compounding can change the figure by a few rupees.

Try it without writing code

If you just want the numbers, there's a free EMI calculator and a loan comparison calculator on Erapse, a site I run. They're handy for sanity-checking your own implementation against.

What would you add to a loan calculator? Prepayment simulation? Floating-rate changes?