How this calculator works
- Step 1Start with unpaid principal₹1,00,000.00Use the outstanding balance, not necessarily the original loan.
- Step 2Apply interest then payment₹2,500.00At a constant nominal 10% annual rate, divided by twelve.
- Step 3Stop when the balance clears49 paymentsThe final payment reduces to ₹2,146.92.
This calculator answers a different question from an EMI calculator: “If I pay this much each month, how long will the balance last?” Interest is charged on the unpaid principal. Each end-of-month payment covers that interest first; the remainder reduces the balance.
The rate and payment stay constant. The answer counts whole monthly payments, not calendar dates. It does not choose an affordable payment or include processing fees, insurance, tax benefits, late charges or rate resets.
Worked example: a fixed monthly payment
- Monthly interest rate
i = annual percentage / 1200- Algebraic duration
n = −ln(1 − principal × i / payment) / ln(1 + i)- Each month’s unpaid balance
closing = opening + opening × i − payment
- paymentchosen monthly amount ₹2,500.00
- nfractional mathematical duration 48.858265 months
- Starting principal₹1,00,000.00
- Chosen monthly payment₹2,500.00
- First-month interest₹833.33
- Final, reduced payment₹2,146.92
- Total interest across the schedule₹22,146.92
- Whole monthly payments needed49
The logarithmic equation gives a fractional mathematical duration. Billing still happens monthly. The worksheet therefore builds a ledger, takes full chosen payments until the last month, then pays only the balance and that month’s interest.
The total payment figure adds the actual ledger payments. It is not the chosen payment multiplied by a fractional duration. Currency is rounded only when displayed; a lender’s paise-by-paise schedule may settle differently.
A payment that does not cover interest cannot clear the loan
The chosen payment needs to exceed first-month interest; equality leaves the principal unchanged.
When payment equals interest, there is nothing left to reduce principal. A smaller payment makes the unpaid balance grow. These cases produce an explicit input error rather than an invented duration or a misleading zero.
Even a payment just above interest can require a very long term. This tool rejects plans beyond 1200 monthly payments. That is a modelling safeguard, not a statement that a lender offers a hundred-year loan.
Compare a larger payment, without assuming affordability
- Default chosen payment49 months₹2,500.00 monthly; total interest ₹22,146.92.
- Higher illustrative payment40 months₹3,000.00 monthly; total interest ₹17,641.61.
A larger payment reduces principal faster and leaves less balance to accrue future interest. The comparison only describes the mathematics. It does not consider your cash needs, emergency reserves, contractual prepayment rules or whether changing the payment is permitted.
Zero interest and an oversized final payment
- Default loan at zero interest40 monthsThe principal is divided by the monthly payment; no logarithm or division by an interest rate is needed.
- Last payment in the default plan₹2,146.92Only the remaining balance and its final month’s interest are paid, rather than another full instalment.
If your chosen payment exceeds principal plus first-month interest, the loan clears with one smaller payment. This model assumes even that payment happens after one full month. A same-day settlement quote needs the lender’s actual accrual rules.
Read and keep the payoff schedule
Check principal, interest and closing balance together; the headline duration alone does not describe the cost.
The full table shows opening principal, actual payment, interest, principal reduction and closing balance. Download CSV for unrounded rows. Near exact payoff, tiny floating-point residuals are treated as numerical noise so they do not create an extra billing month.
The algebraic duration is useful for independent checking. It is not a promise of a specific payoff date. Existing arrears, daily accrual, changing rates or different payment dates require a more detailed model.
Related loan tools
Tenure, EMI and rate are tied together. Fix any two and the third follows.
For the EMI on a set term, use the EMI calculator. The loan prepayment calculator shows how a part-payment shortens the term, and the interest rate calculator finds the rate from a payment.
Common mistakes
Mistake: Enter the original borrowing for a partly repaid loan.
Instead: Start from the current outstanding principal on a consistent date.
Mistake: Compare an EMI with an annual interest amount.
Instead: Use a monthly payment and the nominal yearly rate; the model converts the rate.
Mistake: Multiply full payment by a rounded-up duration to get cost.
Instead: Use the actual final payment and total from the schedule.
Mistake: Assume the result includes a floating-rate reset.
Instead: Recalculate each new fixed-rate scenario or use the lender’s contractual schedule.
Methodology and sources
Tests compare the payoff ledger with a closed-form outstanding balance and reverse existing EMI calculations.
The formulas follow OpenStax’s annuity and loan-amortisation treatment. Independent cases include zero interest, early one-payment payoff and exact whole terms. Review dates, source links and the financial disclaimer appear below.
Read how we test our calculators, or browse more money calculators.