Home Loan Prepayment: Reduce the EMI or the Tenure? The Maths, Worked Through

When you make a part-prepayment on a home loan, the bank usually asks one question: do you want to reduce your EMI, or reduce your tenure? Most people pick the lower EMI because it feels like immediate relief. The numbers say that choice costs a lot of money.

I built the loan calculators in PaisaCalc to answer exactly this kind of question. In this article I'll walk through the formula, then run a realistic loan through the app's actual code so you can see where the interest goes and what a prepayment really saves.

The EMI formula

An EMI (equated monthly instalment) is the fixed monthly payment that pays off a loan, interest included, by the end of its term. The standard formula is:

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

P = loan amount (principal)
r = monthly interest rate = annual rate / 12 / 100
n = number of monthly instalments

In PaisaCalc that is a few lines of TypeScript, with one guard most online examples skip. At a 0% rate the formula divides zero by zero, so the code falls back to a plain split (₹1,20,000 over 12 months is ₹10,000 a month). Zero-interest EMIs are common on phones and appliances, so the case does come up.

export function emi(principal: number, annualRate: number, months: number) {
  if (principal <= 0 || months <= 0) return 0;
  const r = annualRate / 12 / 100;
  if (r === 0) return principal / months;
  const f = Math.pow(1 + r, months);
  return (principal * r * f) / (f - 1);
}

Our example loan

Take a home loan of ₹50 lakh at 8.5% for 20 years (240 months). Plugging that in gives:

• EMI: ₹43,391
• Total interest over 20 years: ₹54,13,879
• Total paid: ₹1,04,13,879, more than double the amount borrowed

Where your EMI actually goes

The EMI stays the same every month, but what it pays for changes. Each month the interest is charged on the outstanding balance; whatever is left of the EMI reduces the principal. PaisaCalc builds the amortisation schedule month by month and adds it up per year:

Look at year 1: of the ₹5.2 lakh you pay, only about ₹1 lakh reduces the loan. More than 80% is interest. Even after ten years you still owe about ₹35 lakh of the original ₹50 lakh. This front-loading is why prepayments made early in a loan are so effective: every rupee of principal you remove early stops generating interest for all the remaining years.

One implementation detail is worth pointing out. Because of floating-point rounding, subtracting the same EMI 240 times leaves a residue of a few paise. The code has the last instalment pay off whatever balance remains, so the schedule always ends at exactly zero.

Prepaying ₹5 lakh: the two options compared

Now suppose that right at the start you pay an extra ₹5 lakh, perhaps from a bonus or a matured deposit. The outstanding balance drops to ₹45 lakh. The bank then gives you a choice:

Same ₹5 lakh, same loan, same day. Reducing the tenure saves more than three times as much interest and finishes the loan 52 months (4 years and 4 months) early. Lowering the EMI frees up about ₹4,300 a month, but the balance falls more slowly, so interest keeps building for the full 20 years.

The code models the two choices simply. "Reduce EMI" recalculates the EMI on the new balance over the original term. "Reduce tenure" keeps the EMI and simulates month by month until the balance reaches zero:

function payDown(balance: number, r: number, payment: number, maxMonths: number) {
  let months = 0;
  let interest = 0;
  while (balance > 0.005 && months < maxMonths) {
    const i = balance * r;
    interest += i;
    balance = balance + i - Math.min(payment, balance + i);
    months++;
  }
  return { months, interest };
}

The maxMonths cap matters. If someone enters a payment that doesn't even cover the monthly interest, the balance never falls and a naive loop would run forever and freeze the app. PaisaCalc checks for that case before simulating.

Small and regular beats nothing

You don't need a lump sum. Paying just ₹5,000 extra every month on the same loan, about 11.5% above the EMI, ends it in 187 months and saves ₹13,89,250 in interest. For many salaried borrowers, a standing instruction for a small extra amount is easier than waiting for a windfall.

Comparing loan offers: don't look at the rate alone

PaisaCalc's loan comparison adds processing fees to the total cost, because a lower rate with a fee isn't always cheaper. For the same ₹50 lakh over 20 years:

• Offer A: 8.4% with a ₹50,000 processing fee: EMI ₹43,075, total cost (interest + fee) ₹53,88,054
• Offer B: 8.6% with no fee: EMI ₹43,708, total cost ₹54,89,953

Over the full term, Offer A is about ₹1 lakh cheaper despite the fee. But if you plan to prepay heavily and close the loan early, there is less time for the lower rate to make up for the fee. That's exactly why it helps to run your own numbers rather than rely on a rule of thumb.

When reducing the EMI is the right call

Reducing the tenure is usually better for the total cost, but not always better for you:

• Your cash flow is tight. If the EMI is a strain, a lower EMI reduces the risk of missing payments, which is far more expensive than extra interest.
• You keep the option open. With a lower EMI you can still pay extra voluntarily whenever you can afford it, which gets you most of the tenure benefit without committing to it.
• Your emergency fund comes first. Money locked into a house can't be withdrawn in a medical emergency. Keep several months of expenses liquid before prepaying aggressively.

Things to check before you prepay

• Prepayment charges: RBI rules bar lenders from charging foreclosure or part-prepayment penalties on floating-rate term loans taken by individuals. Fixed-rate loans can carry charges, so read your sanction letter.
• The tax angle: under the old tax regime, interest on a self-occupied home loan is deductible up to ₹2 lakh a year. Prepaying reduces future interest, so it also reduces that deduction. Under the new regime this deduction isn't available for a self-occupied home.
• The comparison rate: prepaying a loan at 8.5% is effectively a guaranteed, risk-free 8.5% return. Whether that beats investing the money depends on what you would realistically earn after tax, and on how much the certainty is worth to you.

Try it with your own numbers

Every figure in this article came from the same functions that power the EMI, prepayment and loan comparison calculators in PaisaCalc. It's free, runs in the browser, and doesn't ask for any personal details. Enter your outstanding balance, rate and remaining months and compare the two prepayment options yourself before you talk to the bank.