Home Loan EMI Calculator With Part Payment Formula

This home loan EMI calculator estimates the monthly instalment for a fixed-rate loan and shows how an extra part payment changes the balance and interest under a specified recalculation method. Enter the loan amount, annual interest rate, term, part-payment amount, and the month it is paid to see the revised EMI and estimated interest savings.

Formula

The standard EMI formula calculates equal monthly payments for a fixed-rate loan. The part-payment calculation first finds the balance after the stated number of instalments, subtracts the extra payment, then recalculates the EMI over the original remaining term.

• EMI = P × r × (1 + r)ⁿ / [(1 + r)ⁿ − 1], equivalently P × r / [1 − (1 + r)⁻ⁿ].
• B_k = P × (1 + r)^k − EMI × [(1 + r)^k − 1] / r.
• Balance after part payment = B_k − E.
• New EMI = balance × r / [1 − (1 + r)^{−(n − k)}].
• Estimated interest saved = original total scheduled payments − (payments made before part payment + remaining revised payments + part payment).

P is the starting principal in your currency; r is the monthly rate, calculated as annual rate in percent ÷ 1,200; n is the original number of monthly payments; k is the month of the part payment; E is the part-payment amount; and B_k is the balance after k regular payments, immediately before the extra payment. The calculator assumes the part payment is made after that month’s EMI. Money outputs are in your currency.

Worked Example

Using the defaults above: principal P = 5,000,000; annual rate = 8%; term = 20 years, or n = 240 months; part payment E = 500,000 after k = 12 monthly payments. The monthly rate is r = 8 ÷ 1,200 = 0.0066667.

1. Original EMI = 5,000,000 × 0.0066667 ÷ [1 − (1.0066667)⁻²⁴⁰] = 41,822.17.
2. Balance after 12 payments, before the extra payment = 5,000,000 × (1.0066667)¹² − 41,822.17 × [(1.0066667)¹² − 1] ÷ 0.0066667 = approximately 4,864,004.56.
3. Subtract the part payment: 4,864,004.56 − 500,000 = 4,364,004.56.
4. There are 228 months left. Revised EMI = 4,364,004.56 × 0.0066667 ÷ [1 − (1.0066667)⁻²²⁸] = 37,524.49.
5. Estimated interest saved = 41,822.17 × 240 − [41,822.17 × 12 + 37,524.49 × 228 + 500,000] = 591,017.40.

Values are rounded to cents for display; calculations may differ slightly if a lender carries more precision internally or rounds each instalment differently.

Assumptions

• The annual rate stays fixed for the calculation period.
• Payments are monthly and made at the end of each month; the part payment follows the EMI in the selected month.
• Interest accrues monthly at annual APR divided by 12, with no daily-interest adjustment.
• The part payment reduces principal, and the remaining term stays unchanged so the EMI is recalculated.
• Fees, taxes, insurance, PMI, escrow, lender charges, and any prepayment restrictions are not included.

How Part Payment Changes EMI

A part payment is an extra amount applied to the loan principal in addition to the scheduled EMI. Since later interest is calculated on a smaller balance, the total interest can fall. This calculator models one part payment and chooses a lower EMI while keeping the original end date. It does not shorten the term.

A lender may instead keep the EMI unchanged and reduce the remaining repayment period. That approach has a different payoff date and interest result. Some loan contracts may also apply the extra amount according to a different processing date or charge. Check how the servicer will allocate and recalculate a payment before comparing its figures with this estimate.

How to Use and Read the Results

• Enter the current principal, not the original property price or total purchase cost.
• Enter the annual interest rate as a percentage, such as 8 for eight percent, and the full original term in years.
• Enter the extra principal payment and the month in which it occurs. Month 12 means after 12 regular monthly instalments.
• Read the original EMI, balance after the extra payment, revised EMI, and estimated interest saved. A zero part payment leaves the original payment schedule essentially unchanged.

The interest-saved output compares the original scheduled payments with the modeled reduced-EMI schedule, including the extra principal payment. It is an estimate, not a lender payoff quote. If your actual account has already accrued interest, arrears, fees, rate changes, or earlier extra payments, use the current principal balance and the lender’s exact schedule instead; this one-payment model will not reproduce those details.

Common Mistakes and Limits

• Mixing rate units: The formula requires a monthly decimal rate. For an annual rate in percent, divide by 1,200; entering 8 as the monthly rate would be a major unit error.
• Using the wrong balance: A part payment applies to outstanding principal, not necessarily the amount originally borrowed. Ask for the current principal balance if modeling a loan already in progress.
• Assuming every extra payment lowers the EMI: The agreement or lender’s processing choice may instead shorten the term, or apply conditions not represented here.
• Ignoring dates and rounding: Actual interest may depend on exact payment dates, daily accrual, and the lender’s rounding conventions. Cent-rounded estimates can therefore differ from a statement.
• Entering a payment after the term: The calculator rejects a month beyond the original term because no remaining instalments would be available for recalculation.

Use the lender’s disclosed rate, principal, payment allocation, and revised schedule for account-specific figures. The result is an estimate and the lender’s disclosure gives the exact figures.

Frequently Asked Questions

How do I calculate home loan EMI after a part payment?
First calculate the balance after the scheduled payments made before the extra payment, subtract the part payment, then apply the EMI formula to that balance and the remaining months. The calculator shows this same-term method.

Does a part payment reduce EMI or loan tenure?
It can be modelled either way. This calculator keeps the original remaining term and lowers the EMI; a lender may instead keep the EMI and shorten the term. Confirm which treatment applies to your account.

When should I enter the part-payment month?
Enter the number of regular monthly instalments completed before the extra payment, with the assumption that the payment is made after that month’s EMI. A different payment date can change accrued interest.

Why is my lender’s part-payment result different?
Differences can come from the current principal, payment date, daily interest, rounding, rate changes, fees, earlier payments, or a term-reduction rather than EMI-reduction method.

Can I make several part payments with this calculator?
No. It models one extra payment. For several payments, each amount and date must be applied sequentially to the changing balance, or you can use the lender’s amortization schedule.

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in p | Loan amount | - | 5000000 | 1 | 100000000
in apr | Annual interest rate | % | 8 | 0.01 | 100
in yrs | Original loan term | years | 20 | 0.0833 | 50
in extra | Part payment | - | 500000 | 0 | 100000000
in k | Month of part payment | months | 12 | 1 | 600
out emi | Original monthly EMI | - | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out bal | Balance after part payment | - | p * (1 + apr / 1200) ^ k - emi * ((1 + apr / 1200) ^ k - 1) / (apr / 1200) - extra + 0 * sqrt(yrs * 12 - k) | 2
out newemi | Revised EMI, same remaining term | - | round(max(0, bal) * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12 - k)), 2) | 2
out save | Estimated interest saved | - | emi * yrs * 12 - (emi * k + newemi * (yrs * 12 - k) + extra) | 2