What this calculator does
The Tenure Calculator solves the standard loan amortization formula for time: given a loan's principal, its annual interest rate, and the fixed monthly payment you plan to make, it tells you how many months (and years) it takes to pay the loan down to zero, plus the total interest and total amount you'll repay along the way.
The formula
For a loan with principal P, monthly interest rate r (annual rate ÷ 12), and fixed monthly payment M, the number of monthly payments n required is:
n = -ln(1 − P·r / M) / ln(1 + r)
This is the inverse of the standard loan payment formula used for mortgages, auto loans, and personal loans. When the interest rate is 0%, the formula simplifies to n = P / M, since every dollar paid goes straight to principal. The formula assumes a fixed interest rate and a fixed payment amount for the entire tenure — it does not model variable rates, payment holidays, or extra lump-sum payments.
Why the payment has to clear the interest first
Each month, part of the payment covers that month's interest charge (the outstanding balance times r) and the rest reduces the principal. If the monthly payment M is less than or equal to P × r, the payment never covers even the first month's interest, so the balance stays flat or grows instead of shrinking — the loan mathematically never gets paid off. The calculator checks for this and flags it instead of returning a nonsensical result.
Getting accurate results
- Enter the interest rate as an annual percentage (e.g., 7.5 for 7.5%) — the calculator divides it by 12 internally to get the monthly rate used in the formula.
- The monthly payment should be the amount going toward principal and interest only; leave out escrow, insurance, or fees if you want the tenure for the loan itself.
- Because monthly compounding is assumed, results will differ slightly from lenders that compound daily or use a different day-count convention.
Interpreting the output
The reported tenure is the number of equal monthly payments needed to fully amortize the loan. In practice a lender rounds this up to a whole number of payments, so the final payment is often smaller than the rest. Total interest is simply the total of all payments minus the original principal — it grows quickly with a smaller monthly payment (longer tenure) even at the same interest rate, because more of the balance stays outstanding for longer.
Next steps
- Compare tenures at a few different monthly payment levels to see the trade-off between monthly affordability and total interest cost.
- For an actual loan, confirm the tenure and total cost quoted by your lender, since fees, rate type, and compounding conventions can shift the exact numbers.
- Re-run whenever the rate, payment, or remaining balance changes materially.