Estimate the repayment tenure for a loan, given the principal, rate and the EMI you plan to pay.
Uses the EMI formula in reverse, with logarithms, to find the number of months needed.
Tenure: n = ln(EMI ÷ (EMI − P×r)) ÷ ln(1+r)
The loan tenure calculator answers a question most EMI tools skip: if I pay a particular EMI, how long will this loan take to clear? You enter the loan amount, the annual rate and the monthly amount you plan to pay, and it solves for the number of months.
It is useful whenever the EMI is the fixed part of your plan. A salaried borrower may know exactly how much can go to a loan each month. A borrower whose floating rate has risen may want to see how far the bank has stretched the tenure. Someone paying more than the required EMI may want to know how many years that shaves off.
The calculator also warns when the EMI is too small ever to repay the loan, which happens when it does not even cover the monthly interest.
1. Write down the principal P, the annual rate and the EMI you intend to pay.
2. Convert the rate to a monthly rate r = annual rate ÷ 12 ÷ 100.
3. Compute the first month's interest P × r. If the EMI is not larger than this, the loan never reduces.
4. Otherwise compute n = ln(EMI ÷ (EMI − P × r)) ÷ ln(1 + r).
5. Round n up to the next whole month; the last EMI will be smaller than the rest.
6. Divide n by 12 to express the tenure in years and months.
Start from EMI = P × r ÷ (1 − (1 + r)⁻ⁿ). Rearranging gives 1 − (1 + r)⁻ⁿ = P × r ÷ EMI, so (1 + r)⁻ⁿ = 1 − P × r ÷ EMI = (EMI − P × r) ÷ EMI. Taking the reciprocal, (1 + r)ⁿ = EMI ÷ (EMI − P × r). Taking natural logs of both sides and dividing by ln(1 + r) gives n = ln(EMI ÷ (EMI − P × r)) ÷ ln(1 + r). The unknown sits in an exponent, which is why logarithms are needed.
The term EMI − P × r is the principal repaid in the first month. If it is zero, the balance never changes and the loan runs forever. If it is negative, unpaid interest is added and the balance grows. The formula signals this by asking for the log of an infinite or negative number, and the calculator reports that the loan cannot be repaid. When the EMI is only slightly above interest, the tenure becomes very long, because early principal repayment is tiny and the balance falls very slowly.
Because tenure depends on the gap between EMI and interest, a modest increase in EMI can shorten the loan sharply when that gap is small. On a long home loan, paying about 10% more than the required EMI can remove several years. The reverse is also true. When a floating rate rises and the bank keeps your EMI unchanged, the gap narrows and the remaining tenure can jump by years. This calculator shows that effect directly if you enter the new rate with your current EMI.
Farhan owes ₹20,00,000 on a loan at 8.5% a year and can comfortably pay ₹22,000 every month.
Answer: Estimated tenure 146.3 months (12.2 years)
Entering an EMI below the monthly interest and expecting a finite answer.
Rounding the month count down, which leaves a small balance unpaid.
Using the original loan amount after years of repayment instead of the current outstanding balance.
Forgetting that the bank may cap the tenure at your retirement age, whatever the formula says.
Finding out how long a loan will run if the EMI is fixed by budget.
Checking how much a floating-rate rise has extended the remaining tenure.
Seeing how many years an EMI step-up would save.
Planning when a loan will end relative to a child's college or retirement.
Why does it say my EMI can never repay the loan?
If your chosen EMI is equal to or less than the monthly interest on your loan, your loan amount never goes down. You would be paying interest forever, without ever touching the actual loan. Your EMI must be more than the monthly interest for the loan to be paid off.